analog and mixed-signal design for soc in emerging digital...
TRANSCRIPT
1
EE 435
Lecture 8:
High-Gain Single-Stage Op Amps
2
Basic Op Amp Design
• Fundamental Amplifier Design Issues
• Single-Stage Low Gain Op Amps
• Single-Stage High Gain Op Amps
• Other Basic Gain Enhancement Approaches
• Two-Stage Op Amp
Review from Last Lecture
3
Determination of op amp characteristics
from quarter circuit characteristics
VDD
F
P
F
P
VSS
2
dv
2
dv
VBB VBB
VO+ VO
-
IBB
VDD
F
P
F
P
F
P
F
P
VSS
2
dv
2
dv
VBB VBB
VO+ VO
-
IBB
V1G M1V1 G 1
V1G M1 G 1
G2
CL
2
Vd
Vo++
21L
M1
d
OV
GGsC2
G
V
VA
L
M1
L
21
21
M1VO
2C
GGB
C
GGBW
GG2
GA
Small signal differential half-circuit
Recall from a previous lecture:
4
Single-Stage High Gain Op Amps
How can the gain of the op amp be increased?
21
M1VO
GG
GA
2
1
Recall from Quarter-Circuit Concept
A possible strategy :
Increase GM1 or Decrease G1 (and G2)
in Quarter Circuit or Both
Review from Last Lecture
5
Single-Stage High-Gain Op Amps
• If the output conductance can be
decreased without changing the
transconductance, the gain can be
enhanced
• Will concentrate on quarter-circuits and
extend to op amps
Review from Last Lecture
6
Determination of 2-port parameters
gO2
gM2
V1
V1 g
O1
gM1
V2
V2
General Two-Port Network
VTST
CL
O2L
M2
TST
2
TSTM2LO22
gsC
g
sV
sVsA
0VgsCgV
0L
0
bsC
asA
Background
Determination of {go1, go2,gM1,gM2 }
Method 2 Load Termination Approach
Since first-order express the gain A(s) in form
gO2
gM2
V1
V1 g
O1
gM1
V2
V2
General Two-Port Network
VTST
CL
observe
(must express with coefficient of s in den equal to CL)
Review from Last Lecture
7
o2OUTXm2INm1o2o1X
o2XXm2Lo2OUT
gVVgVgggV
gVVgsCgV
M1
VIN
M2
VOUT
CL
IN1
X2
o2OUT2m21m1o2o1X
o2X2m2Lo2OUT
VV
VV
gVVgVgggV
gVVgsCgV
Analysis of Cascode AmplifierBackground
m1 o2 m2OUT m1 m2
IN L o1 o2 m2 o1 o2 L m2 o1 o2
g g gV g g
V sC g g g g g sC g g g
m2
o2o1L
m1
IN
OUT
g
ggsC
g
V
V gMEQ
gOEQ
Review from Last Lecture
8
High output impedance quarter-circuits
VSS
CLM2
M1
IDB
VDD
VBB
VOUT
VIN
Cascode Amplifier
Output conductance appears to have been
decreased !1
21
2
1 20
1 2
1
( ) mv
oL o
m
m mV
o o
m
L
gA s
gsC g
g
g gA
g g
gGB
C
But must verify in the practical parameter
domain to be sure!
O2OEQ O1
m2
mEQ m1
gg g
g
g g
Review from Last Lecture
9
High output impedance quarter-circuits
EB
V0λV
2A
Cascode AmplifierSubstantial increase in dc gain
No improvement in GB but also
no deterioration in GB !
How does this compare with previous amplifier
using single transistor as quarter circuit?
EBLDD V
1
CV
2PGB
m1
L
gGB
C
VSS
CLM2
M1
IDB
VDD
VBB
VOUT
VIN
1 20
1 2
m mV
o o
g gA
g g
0
1 EB1 2 EB2
DD L EB1
2 2•
λ V λ V
2P 1•
V C V
VA
GB
Cascode amplifier quarter circuit:
Single transistor quarter circuit:
Review from Last Lecture
10
High output impedance quarter-circuits
Cascode Amplifier
(small-signal equiv)
Quarter Circuit
M3
M1
VOUT
VIN
11
High output impedance quarter-circuits
Cascode Amplifier
Quarter Circuit
M5
M7
VDD
VB1
VB2
Counterpart Circuit
M3
M1
VOUT
VIN
VB3
12
Telescopic Cascode Op Amp
Needs CMFB Circuit for VB1 or VB5
Either single-ended or differential outputs
Can connect counterpart as current mirror to eliminate CMFB
M3
M1
VOUT
VIN
VDD
VSS
VB5 M
11
VB1
IT
VINVIN
M1M2
M3 M4
M5
M7
M6
M8
VB2
VB3
VOUT
CL
13
Determination of op amp characteristics from quarter circuit
characteristics (for single-ended gain)
FVIN
IXX
VOUT
VSS
CL
Note: Factor of 4 reduction of single-ended gain
VDD
F
P
F
P
VSS
2
dv
2
dv
VBB VBB
IBB
VDD
F
P
F
P
F
P
F
P
VSS
2
dv
2
dv
VBB VBB
IBB
CL CL
VO-VO- VO
+VO+
1 2
3 4
Small signal Quarter Circuit Small signal differential amplifier
Recall:
1
0
1 3
1 3
1
1
1 3
2
2
2
M
V
L
M
L
M
L
G
AG G
G GBW
C
GGB
C
G
A ssC G G
0M
V QC
L
M
L
M
L
GA
G
GBW
C
GGB
C
GA s
sC G
14
Telescopic Cascode Op Amp
Single-ended operation
VDD
VSS
VB5 M
11
VB1
IT
VINVIN
M1M2
M3 M4
M5
M7
M6
M8
VB2
VB3
VOUT
CL
gOQC =
gOCC =
gmQC =
15
Telescopic Cascode Op Amp
L
m
C
gGB
2
1
Single-ended operation
m1
oo3 o7
o1 o5m3 m7
g-
2A =g g
g + gg g
VDD
VSS
VB5 M
11
VB1
IT
VINVIN
M1M2
M3 M4
M5
M7
M6
M8
VB2
VB3
VOUT
CL
m1
do3 o7
L o1 o5m3 m7
g-
2A s =g g
sC g + gg g
16
Telescopic Cascode Op Amp
L
m
C
gGB
2
1
Single-ended operation
m1
oo3 o7
o1 o5m3 m7
g-
2A =g g
g + gg g
This circuit is widely used !!(CMFB circuit not shown)
VDD
VSS
VB5 M
11
VB1
IT
VINVIN
M1M2
M3 M4
M5
M7
M6
M8
VB2
VB3
VOUT
CL
m1
do3 o7
L o1 o5m3 m7
g-
2A s =g g
sC g + gg g
• Large improvement in A0
• No change in GB
17
Telescopic Cascode Op Amp
(CMFB circuit not shown)
VSS
VB5
VB1
VINVIN
M1M2
M3 M4
M5
M7
M6
M8
VB2
VB3
VOUT
CL
M11M12
IB
IT
VDD
Current Mirror Bias
VDD
• One tail bias current generator shown
• IT often one of many outputs for current mirror
• IB and M12 often common to many blocks
• IB often generated from a reference generator circuit
• Tail voltage bias can also be used
19
Telescopic Cascode Op Amp
• Current-Mirror p-channel Bias to Eliminate CMFB
• Only single-ended output available
• Doubles dc gain
VSS
VB5
VINVIN
M1M2
M3 M4
M5
M7
M6
M8
VB3
VOUT
CL
M11M12
IB
IT
VDD
Current Mirror Bias
VDD
VSS
VB5
VINVIN
M1M2
M3 M4
M5
M7
M6
M8
VB3
VOUT
CL
M11M12
IB
IT
VDD
Current Mirror Bias
VDD
VB2
Standard p-channel Cascode Mirror Wide-Swing p-channel Cascode Mirror
20
Telescopic Cascode Op Amp
VSS
VB5
VB1
VINVIN
M1M2
M3 M4
M5
M7
M6
M8
VB2
VB3
VOUT
CL
M11M12
IB
IT
VDD
Current Mirror Bias
VDD
m1
do3 o7
L o1 o5m3 m7
g-
2A s =g g
sC g + gg g
VSS
VB5
VINVIN
M1M2
M3 M4
M5
M7
M6
M8
VB3
VOUT
CL
M11M12
IB
IT
VDD
Current Mirror Bias
VDD
m1d
o3 o7L o1 o5
m3 m7
-gA s =
g gsC g + g
g g
?
(CMFB circuit needed)(No CMFB circuit needed)
21
Telescopic Cascode Op Amp
• Differential Output
• CMFB to establish VB1 or VB5 needed
• Tail current generally generated with current mirror
VB1
IT
VIN VIN
M1M2
M3 M4
M5
M7
M6
M8
VB2
VB3
CLCL
+OUTV
-OUT
V
VDD
VB5
VSS
M11
22
Telescopic Cascode Op Amp
Signal Swing and Power Supply Limitations
Thus, there are a minimum of 5 VDSAT
drops between VDD and VSS
This establishes a lower bound on VDD-
VSS and it will be further reduced by the
p-p signal swing required on the output
VSS
VB1
VINVIN
M1 M2
M3 M4
M5
M7
M6
M8
VB2
VB3
VOUT
CL
M11
IT
VDD
VB5
VDSAT
VDSAT
VDSAT
VDSAT
VDSAT
There are a minimum of 2 VDSAT drops
between VOUT and VDD and a minimum of 3
VDSAT drops between VOUT and VSS
23
Telescopic Cascode Op Amp
VB1
IT
VIN VIN
M1M2
M3 M4
M5
M7
M6
M8
VB2
VB3
CLCL
+OUTV
-OUT
V
VDD
VB5
VSS
M11
IT
VIN VINM1
M2
M3 M4
M5
M7
M6
M8
VB2
VB3
CLCL
+OUTV
-OUT
V
VDD
VSS
VB1
VB5
M11
n-channel inputs p-channel inputs
How important is it to develop good approximate analysis methods for an op amp with the complexity of the telescopic cascade structure?
And many useful op amp circuits will have more complexity !!
VSS
VB5
VINVIN
M1M2
M3 M4
M5
M7
M6
M8
VB3
VOUT
CL
M11M12
IB
IT
VDD
Current Mirror Bias
VDD
Telescopic Cascode Op Amp with Mirror-connected Counterpart Circuit
• Previous analysis obtained almost by inspection• Gain expressions were real simple• Gain expressions provide major insight into operation• Some assumptions were made to simplify analysis
⁻ Vac=0 at “approximate axis of symmetry”⁻ Matched left and right side transistors⁻ Current mirror used to mirror left-side current to right side
How much more involved would an exact analysis be ?Would an exact analysis provide additional insight ?
Vgs1
gm1Vgs1
g01
Vgs3
gm3Vgs3
g03
V-INVgs2
gm2Vgs2
g02
Vgs4
gm4Vgs4
g04
V+
IN
CL
VOUT
VS8
Vgs11
gm11Vgs11
g011
VS1
Vgs7
gm7Vgs7
g07
Vgs5
gm5Vgs5
g05
Vgs8
gm8Vgs8
g08
Vgs6
gm6Vgs6
g06
VS7
VG7
VS4VS3
Small-Signal model of Telescopic Cascode Amplifier
A bit tedious to obtain but really straight forward
1 01 02 011 3 01 4 02 1 1 2 1
3 01 03 1 1 01 1 03 7 3 3
4 02 04 2 1 02 1 04 4 4
04 08 4 4 7 8 04 4 08 88
7 07 03
S S S m IN S m IN S
S m IN S S G m S
S m IN S S OUT m S
OUT L m S G S S Sm
G m
V g g g V g V g g V V g V V
V g g g V V g V g V g V
V g g g V V g V g V g V
V sC g g g V g V V g V g V
V g g g
7 7 7 3 3 03 3 07 7
8 06 08 8 7 8 7 8 08
7 05 07 5 7 7 7 7 07 7
G S m S S S
S m S m G S OUT
S m S m G S G
V V g V g V g V
V g g g V g V V V g
V g g g V g V V g V
Analysis of Telescopic Cascode Amplifier
Apply KCL at 7 nodes to obtain a set of 7 independent linear equations
A bit tedious to obtain but really straight forward
Time required to obtain set of equations is quite small
1 01 02 011 3 01 4 02 1 1 2 1
3 01 03 1 1 01 1 03 7 3 3
4 02 04 2 1 02 1 04 4 4
04 08 4 4 7 8 04 4 08 88
7 07 03
S S S m IN S m IN S
S m IN S S G m S
S m IN S S OUT m S
OUT L m S G S S Sm
G m
V g g g V g V g g V V g V V
V g g g V V g V g V g V
V g g g V V g V g V g V
V sC g g g V g V V g V g V
V g g g
7 7 7 3 3 03 3 07 7
8 06 08 8 7 8 7 8 08
7 05 07 5 7 7 7 7 07 7
G S m S S S
S m S m G S OUT
S m S m G S G
V V g V g V g V
V g g g V g V V V g
V g g g V g V V g V
Analysis of Telescopic Cascode Amplifier
Apply KCL at 7 nodes to obtain a set of 7 independent linear equations
111 12 13 1 2
321 22 26 1
31 33 37 4 2
43 45 46 47 7
52 54 56 8
64 65 66 67 7
74 76
0
0
0 0
0 0
0 0
0 0
S m m
S m
S m
IN
S
INS
G
OUT
Va a a g g
Va a a g
a a a V gV
a a a a VV
a a a V
a a a a V
a a V
In matrix form, this looks like (0 in blank locations)
INA V G V
1
INV A G V
• The A matrix has many 0’s which dramatically reduces complexity of solution• But there are still a large number of off-diagonal terms
Analytical solution of these equations is not practical
%Complete Analysis of Telescopic Cascode Op Amp
diary('matlabdiary')
clear
clc
fprintf('Complete Analysis of Telescopic Cascode Op Amp')
syms Av s CL VOUT VS1 VS3 VS4 VS7 VS8 VG7 Vinn Vinp g01 g02 g03 g04 g05
g06 g07 g08 g011 gm1 gm2 gm3 gm4 gm5 gm6 gm7 gm8
eqn1 =VS1*(gm1+gm2+g01+g02+g011)==VS3*g01+VS4*g02+Vinp*gm1+gm2*Vinn;
eqn2 = VS3*(gm3+g01+g03)+gm1*Vinp==VS1*(g01+gm1)+VG7*g03;
eqn3 = VS4*(gm4+g02+g04)+Vinn*gm2==VS1*(gm2+g02)+VOUT*g04;
eqn4 = VOUT*(s*CL+g04+g08)+VG7*gm8==VS4*(gm4+g04)+VS8*(gm8+g08);
eqn5 = VG7*(gm7+g07+g03)==VS3*(gm3+g03)+VS7*(gm7+g07);
eqn6 = VS8*(gm8+g06+g08)+VS7*gm8==VG7*gm8+VOUT*g08;
eqn7 = VS7*(gm7+gm5+g05+g07)==VG7*(gm7+g07);
eqn8 = Av==VOUT/Vinp;
sol=solve([eqn1,eqn2,eqn3,eqn4,eqn5,eqn6,eqn7,eqn8],[VOUT,VS1,VS3,VS4,VS7,
VS8,VG7,Av]);
VOUTX=sol.VOUT
collect(VOUTX,Vinn)
Simple program and effort to write program is small
fprintf('Differential Analysis of Telescopic Cascode Op Amp')
syms Av s CL VOUT VS1 VS3 VS4 VS7 VS8 VG7 Vdiff g01 g02 g03 g04 g05 g06 g07 g08 g011 gm1 gm2 gm3
gm4 gm5 gm6 gm7 gm8
eqn1 =VS1*(gm1+gm2+g01+g02+g011)==VS3*g01+VS4*g02+Vdiff*gm1/2-gm2*Vdiff/2;
eqn2 = VS3*(gm3+g01+g03)+gm1*Vdiff/2==VS1*(g01+gm1)+VG7*g03;
eqn3 = VS4*(gm4+g02+g04)-Vdiff*gm2/2==VS1*(gm2+g02)+VOUT*g04;
eqn4 = VOUT*(s*CL+g04+g08)+VG7*gm8==VS4*(gm4+g04)+VS8*(gm8+g08);
eqn5 = VG7*(gm7+g07+g03)==VS3*(gm3+g03)+VS7*(gm7+g07);
eqn6 = VS8*(gm8+g06+g08)+VS7*gm8==VG7*gm8+VOUT*g08;
eqn7 = VS7*(gm7+gm5+g05+g07)==VG7*(gm7+g07);
eqn8 = Av==VOUT/Vdiff;
sol=solve([eqn1,eqn2,eqn3,eqn4,eqn5,eqn6,eqn7,eqn8],[VOUT,VS1,VS3,VS4,VS7,VS8,VG7,Av]);
VOUTX=sol.VOUT;
GainAv=sol.Av
collect(GainAv,s)
Simple program and effort to write program is small
VOUTX =
(-(g01*g03*g04*g07*gm2*gm8^2 + g01*g03*g04*gm2*gm7*gm8^2 + g01*g03*g07*gm2*gm4*gm8^2 +
g01*g04*g07*gm2*gm3*gm8^2 + g03*g04*g07*gm1*gm2*gm8^2 + g01*g03*gm2*gm4*gm7*gm8^2 +
g01*g04*gm2*gm3*gm7*gm8^2 + g01*g07*gm2*gm3*gm4*gm8^2 + g03*g04*gm1*gm2*gm7*gm8^2 +
g03*g07*gm1*gm2*gm4*gm8^2 + g04*g07*gm1*gm2*gm3*gm8^2 + g01*gm2*gm3*gm4*gm7*gm8^2 +
g03*gm1*gm2*gm4*gm7*gm8^2 + g04*gm1*gm2*gm3*gm7*gm8^2 + g07*gm1*gm2*gm3*gm4*gm8^2 +
gm1*gm2*gm3*gm4*gm7*gm8^2 + g01*g03*g04*g05*g06*g07*gm2 + g01*g03*g04*g05*g07*g08*gm2 +
g01*g03*g04*g05*g06*g011*gm2 + g01*g03*g04*g05*g08*g011*gm2 + g01*g03*g04*g06*g07*g011*gm2 +
g01*g03*g04*g07*g08*g011*gm2 + g01*g04*g05*g06*g07*g011*gm2 + g01*g04*g05*g07*g08*g011*gm2 +
g03*g04*g05*g06*g07*g011*gm2 + g03*g04*g05*g07*g08*g011*gm2 + g01*g03*g04*g05*g06*gm2*gm7 +
g01*g03*g04*g06*g07*gm2*gm5 + g01*g03*g05*g06*g07*gm2*gm4 + g01*g04*g05*g06*g07*gm2*gm3 +
g03*g04*g05*g06*g07*gm1*gm2 + g01*g03*g04*g05*g06*gm2*gm8 + g01*g03*g04*g05*g07*gm2*gm8 +
g01*g03*g04*g05*g08*gm2*gm7 + g01*g03*g04*g07*g08*gm2*gm5 + g01*g03*g05*g07*g08*gm2*gm4 +
g01*g04*g05*g07*g08*gm2*gm3 + g03*g04*g05*g07*g08*gm1*gm2 + g01*g03*g04*g06*g07*gm2*gm8 +
g01*g03*g04*g06*g011*gm2*gm5 + g01*g03*g05*g06*g011*gm2*gm4 + g01*g03*g04*g07*g08*gm2*gm8 +
g01*g03*g04*g05*g011*gm2*gm8 + g01*g03*g04*g06*g011*gm2*gm7 + g01*g03*g04*g08*g011*gm2*gm5 +
g01*g03*g05*g08*g011*gm2*gm4 + g01*g03*g06*g07*g011*gm2*gm4 + g01*g03*g04*g07*g011*gm2*gm8 +
g01*g03*g04*g08*g011*gm2*gm7 + g01*g03*g07*g08*g011*gm2*gm4 + g01*g04*g05*g06*g011*gm2*gm7 +
g01*g04*g06*g07*g011*gm2*gm5 + g01*g05*g06*g07*g011*gm2*gm4 + g01*g04*g05*g07*g011*gm2*gm8 +
g01*g04*g05*g08*g011*gm2*gm7 + g01*g04*g07*g08*g011*gm2*gm5 + g01*g05*g07*g08*g011*gm2*gm4 +
g03*g04*g05*g06*g011*gm2*gm7 + g03*g04*g06*g07*g011*gm2*gm5 + g03*g05*g06*g07*g011*gm2*gm4 +
g04*g05*g06*g07*g011*gm2*gm3 + g03*g04*g05*g07*g011*gm2*gm8 + g03*g04*g05*g08*g011*gm2*gm7 +
g03*g04*g07*g08*g011*gm2*gm5 + g03*g05*g07*g08*g011*gm2*gm4 + g04*g05*g07*g08*g011*gm2*gm3 +
g01*g03*g04*g06*gm2*gm5*gm7 + g01*g03*g05*g06*gm2*gm4*gm7 + g01*g03*g06*g07*gm2*gm4*gm5 +
g01*g04*g05*g06*gm2*gm3*gm7 + g01*g04*g06*g07*gm2*gm3*gm5 + g01*g05*g06*g07*gm2*gm3*gm4 +
g03*g04*g05*g06*gm1*gm2*gm7 + g03*g04*g06*g07*gm1*gm2*gm5 + g03*g05*g06*g07*gm1*gm2*gm4 +
g04*g05*g06*g07*gm1*gm2*gm3 + g01*g03*g04*g06*gm2*gm5*gm8 + g01*g03*g05*g06*gm2*gm4*gm8 +
g01*g04*g05*g06*gm2*gm3*gm8 + g03*g04*g05*g06*gm1*gm2*gm8 + g01*g03*g04*g05*gm2*gm7*gm8 +
g01*g03*g04*g07*gm2*gm5*gm8 + g01*g03*g04*g08*gm2*gm5*gm7 + g01*g03*g05*g07*gm2*gm4*gm8 +
g01*g03*g05*g08*gm2*gm4*gm7 + g01*g03*g07*g08*gm2*gm4*gm5 + g01*g04*g05*g07*gm2*gm3*gm8 +
g01*g04*g05*g08*gm2*gm3*gm7 + g01*g04*g07*g08*gm2*gm3*gm5 + g01*g05*g07*g08*gm2*gm3*gm4 +
g03*g04*g05*g07*gm1*gm2*gm8 + g03*g04*g05*g08*gm1*gm2*gm7 + g03*g04*g07*g08*gm1*gm2*gm5 +
g03*g05*g07*g08*gm1*gm2*gm4 + g04*g05*g07*g08*gm1*gm2*gm3 + g01*g03*g04*g06*gm2*gm7*gm8 +
g01*g03*g06*g07*gm2*gm4*gm8 + g01*g04*g06*g07*gm2*gm3*gm8 + g03*g04*g06*g07*gm1*gm2*gm8 +
g01*g03*g06*g011*gm2*g\\\r\nm4*gm5 + g01*g03*g04*g08*gm2*gm7*gm8 + g01*g03*g07*g08*gm2*gm4*gm8 +
g01*g04*g07*g08*gm2*gm3*gm8 + g03*g04*g07*g08*gm1*gm2*gm8 + g01*g03*g04*g011*gm2*gm5*gm8 +
g01*g03*g05*g011*gm2*gm4*gm8 + g01*g03*g06*g011*gm2*gm4*gm7 + g01*g03*g08*g011*gm2*gm4*gm5 +
g01*g03*g04*g011*gm2*gm7*gm8 + g01*g03*g07*g011*gm2*gm4*gm8 + g01*g03*g08*g011*gm2*gm4*gm7 +
g01*g04*g06*g011*gm2*gm5*gm7 + g01*g05*g06*g011*gm2*gm4*gm7 + g01*g06*g07*g011*gm2*gm4*gm5 +
g01*g04*g05*g011*gm2*gm7*gm8 + g01*g04*g07*g011*gm2*gm5*gm8 + g01*g04*g08*g011*gm2*gm5*gm7 +
g01*g05*g07*g011*gm2*gm4*gm8 + g01*g05*g08*g011*gm2*gm4*gm7 + g01*g07*g08*g011*gm2*gm4*gm5 +
g03*g04*g06*g011*gm2*gm5*gm7 + g03*g05*g06*g011*gm2*gm4*gm7 + g03*g06*g07*g011*gm2*gm4*gm5 +
g04*g05*g06*g011*gm2*gm3*gm7 + g04*g06*g07*g011*gm2*gm3*gm5 + g05*g06*g07*g011*gm2*gm3*gm4 +
g03*g04*g05*g011*gm2*gm7*gm8 + g03*g04*g07*g011*gm2*gm5*gm8 + g03*g04*g08*g011*gm2*gm5*gm7 +
g03*g05*g07*g011*gm2*gm4*gm8 + g03*g05*g08*g011*gm2*gm4*gm7 + g03*g07*g08*g011*gm2*gm4*gm5 +
g04*g05*g07*g011*gm2*gm3*gm8 + g04*g05*g08*g011*gm2*gm3*gm7 + g04*g07*g08*g011*gm2*gm3*gm5 +
g05*g07*g08*g011*gm2*gm3*gm4 + g01*g03*g06*gm2*gm4*gm5*gm7 + g01*g04*g06*gm2*gm3*gm5*gm7 +
g01*g05*g06*gm2*gm3*gm4*gm7 + g01*g06*g07*gm2*gm3*gm4*gm5 + g03*g04*g06*gm1*gm2*gm5*gm7 +
g03*g05*g06*gm1*gm2*gm4*gm7 + g03*g06*g07*gm1*gm2*gm4*gm5 + g04*g05*g06*gm1*gm2*gm3*gm7 +
g04*g06*g07*gm1*gm2*gm3*gm5 + g05*g06*g07*gm1*gm2*gm3*gm4 + g01*g03*g06*gm2*gm4*gm5*gm8 +
g01*g04*g06*gm2*gm3*gm5*gm8 + g01*g05*g06*gm2*gm3*gm4*gm8 + g03*g04*g06*gm1*gm2*gm5*gm8 +
g03*g05*g06*gm1*gm2*gm4*gm8 + g04*g05*g06*gm1*gm2*gm3*gm8 + g01*g03*g04*gm2*gm5*gm7*gm8 +
g01*g03*g05*gm2*gm4*gm7*gm8 + g01*g03*g07*gm2*gm4*gm5*gm8 + g01*g03*g08*gm2*gm4*gm5*gm7 +
g01*g04*g05*gm2*gm3*gm7*gm8 + g01*g04*g07*gm2*gm3*gm5*gm8 + g01*g04*g08*gm2*gm3*gm5*gm7 +
g01*g05*g07*gm2*gm3*gm4*gm8 + g01*g05*g08*gm2*gm3*gm4*gm7 + g01*g07*g08*gm2*gm3*gm4*gm5 +
g03*g04*g05*gm1*gm2*gm7*gm8 + g03*g04*g07*gm1*gm2*gm5*gm8 + g03*g04*g08*gm1*gm2*gm5*gm7 +
g03*g05*g07*gm1*gm2*gm4*gm8 + g03*g05*g08*gm1*gm2*gm4*gm7 + g03*g07*g08*gm1*gm2*gm4*gm5 +
g04*g05*g07*gm1*gm2*gm3*gm8 + g04*g05*g08*gm1*gm2*gm3*gm7 + g04*g07*g08*gm1*gm2*gm3*gm5 +
g05*g07*g08*gm1*gm2*gm3*gm4 + g01*g03*g06*gm2*gm4*gm7*gm8 + g01*g04*g06*gm2*gm3*gm7*gm8 +
g01*g06*g07*gm2*gm3*gm4*gm8 + g03*g04*g06*gm1*gm2*gm7*gm8 + g03*g06*g07*gm1*gm2*gm4*gm8 +
g04*g06*g07*gm1*gm2*gm3*gm8 + g01*g03*g08*gm2*gm4*gm7*gm8 + g01*g04*g08*gm2*gm3*gm7*gm8 +
g01*g07*g08*gm2*gm3*gm4*gm8 + g03*g04*g08*gm1*gm2*gm7*gm8 + g03*g07*g08*gm1*gm2*gm4*gm8 +
g04*g07*g08*gm1*gm2*gm3*gm8 + g01*g03*g011*gm2*gm4*gm5*gm8 + g01*g03*g011*gm2*gm4*gm7*gm8 +
g01*g06*g011*gm2*gm4*gm5*gm7 + g01*g04*g011*gm2*gm5*gm7*gm8 + g01*g05*g011*gm2*gm4*gm7*gm8 +
g01*g07*g011*gm2*gm4*gm5*gm8 + g01*g08*g011*gm2*gm4*gm5*gm7 + g03*g06*g011*gm2*gm4*gm5*gm7 +
MATLAB simulation results using Symbolic Math Toolbox
MATLAB Solution:
Analysis with Vin+ and Vin-
g04*g06*g011*gm2*gm3*gm5*gm7 + g05*g06*g011*gm2*gm3*gm4*gm7 + g06*g07*g011*gm2*gm3*gm4*gm5 +
g03*g04*g011*gm2*gm5*gm7*gm8 + g03*g05*g011*gm2*gm4*gm7*gm8 + g03*g07*g011*gm2*gm4*gm5*gm8 +
g03*g08*g011*gm2*gm4*gm5*gm7 + g04*g05*g011*gm2*gm3*gm7*gm8 + g04*g07*g011*gm2*gm3*gm5*gm8 +
g04*g08*g011*gm2*gm3*gm5*gm7 + g05*g07*g011*gm2*gm3*gm4*gm8 + g05*g08*g011*gm2*gm3*gm4*gm7 +
g07*g08*g011*gm2*gm3*gm4*gm5 + g01*g06*gm2*gm3*gm4*gm5*gm7 + g03*g06*gm1*gm2*gm4*gm5*gm7 +
g04*g06*gm1*gm2*gm3*gm5*gm7 + g05*g06*gm1*gm2*gm3*gm4*gm7 + g06*g07*gm1*gm2*gm3*gm4*gm5 +
g01*g06*gm2*gm3*gm4*gm5*gm8 + g03*g06*gm1*gm2*gm4*gm5*gm8 + g04*g06*gm1*gm2*gm3*gm5*gm8 +
g05*g06*gm1*gm2*gm3*gm4*gm8 + g01*g03*gm2*gm4*gm5*gm7*gm8 + g01*g04*gm2*gm3*gm5*gm7*gm8 +
g01*g05*gm2*gm3*gm4*gm7*gm8 + g01*g07*gm2*gm3*gm4*gm5*gm8 + g01*g08*gm2*gm3*gm4*gm5*gm7 +
g03*g04*gm1*gm2*gm5*gm7*gm8 + g03*g05*gm1*gm2*gm4*gm7*gm8 + g03*g07*gm1*gm2*gm4*gm5*gm8 +
g03*g08*gm1*gm2*gm4*gm5*gm7 + g04*g05*gm1*gm2*gm3*gm7*gm8 + g04*g07*gm1*gm2*gm3*gm5*gm8 +
g04*g08*gm1*gm2*gm3*gm5*gm7 + g05*g07*gm1*gm2*gm3*gm4*gm8 + g05*g08*gm1*gm2*gm3*gm4*gm7 +
g07*g08*gm1*gm2*gm3*gm4*gm5 + g01*g06*gm2*gm3*gm4*gm7*gm8 + g03*g06*gm1*gm2*gm4*gm7*gm8 +
g04*g06*gm1*gm2*gm3*gm7*gm8 + g06*g07*gm1*gm2*gm3*gm4*gm8 + g01*g08*gm2*gm3*gm4*gm7*gm8 +
g03*g08*gm1*gm2*gm4*gm7*gm8 + g04*g08*gm1*gm2*gm3*gm7*gm8 + g07*g08*gm1*gm2*gm3*gm4*gm8 +
g01*g011*gm2*gm4*gm5*gm7*gm8 + g06*g011*gm2*gm3*gm4*gm5*gm7 + g03*g011*gm2*gm4*gm5*gm7*gm8 +
g04*g011*gm2*gm3*gm5*gm7*gm8 + g05*g011*gm2*gm3*gm4*gm7*gm8 + g07*g011*gm2*gm3*gm4*gm5*gm8 +
g08*g011*gm2*gm3*gm4*gm5*gm7 + g06*gm1*gm2*gm3*gm4*gm5*gm7 + g06*gm1*gm2*gm3*gm4*gm5*gm8 +
g01*gm2*gm3*gm4*gm5*gm7*gm8 + g03*gm1*gm2*gm4*gm5*gm7*gm8 + g04*gm1*gm2*gm3*gm5*gm7*gm8 +
g05*gm1*gm2*gm3*gm4*gm7*gm8 + g07*gm1*gm2*gm3*gm4*gm5*gm8 + g08*gm1*gm2*gm3*gm4*gm5*gm7 +
g06*gm1*gm2*gm3*gm4*gm7*gm8 + g08*gm1*gm2*gm3*gm4*gm7*gm8 + g011*gm2*gm3*gm4*gm5*gm7*gm8 +
gm1*gm2*gm3*gm4*gm5*gm7*gm8)/(g01*g02*g03*g04*g07*gm8^2 + g01*g02*g03*g04*gm7*gm8^2 +
g01*g02*g04*g07*gm3*gm8^2 + g02*g03*g04*g07*gm1*gm8^2 + g01*g02*g04*gm3*gm7*gm8^2 +
g02*g03*g04*gm1*gm7*gm8^2 + g02*g04*g07*gm1*gm3*gm8^2 + g02*g04*gm1*gm3*gm7*gm8^2 +
g01*g02*g03*g04*g05*g06*g07 + g01*g02*g03*g04*g05*g06*g08 + g01*g02*g03*g04*g05*g07*g08 +
g01*g02*g03*g04*g06*g07*g08 + g01*g02*g03*g04*g05*g06*g011 + g01*g02*g03*g05*g06*g07*g08 +
g01*g02*g04*g05*g06*g07*g08 + g01*g02*g03*g04*g05*g08*g011 + g01*g02*g03*g04*g06*g07*g011 +
g01*g03*g04*g05*g06*g07*g08 + g02*g03*g04*g05*g06*g07*g08 + g01*g02*g03*g04*g07*g08*g011 +
g01*g02*g03*g05*g06*g08*g011 + g01*g02*g04*g05*g06*g07*g011 + g01*g02*g03*g06*g07*g08*g011 +
g01*g02*g04*g05*g07*g08*g011 + g01*g03*g04*g05*g06*g08*g011 + g02*g03*g04*g05*g06*g07*g011 +
g01*g02*g05*g06*g07*g08*g011 + g01*g03*g04*g06*g07*g08*g011 + g02*g03*g04*g05*g07*g08*g011 +
g01*g04*g05*g06*g07*g08*g011 + g02*g03*g05*g06*g07*g08*g011 + g03*g04*g05*g06*g07*g08*g011 +
g01*g02*g03*g04*g05*g06*gm7 + g01*g02*g03*g04*g06*g07*gm5 + g01*g02*g04*g05*g06*g07*gm3 +
g02*g03*g04*g05*g06*g07*gm1 + g01*g02*g03*g04*g05*g06*gm8 + g01*g02*g03*g04*g06*g08*gm5 +
g01*g02*g03*g05*g06*g08*gm4 + g01*g03*g04*g05*g06*g08*gm2 + g01*g02*g03*g04*g05*g07*gm8 +
g01*g02*g03*g04*g05*g08*gm7 + g01*g02*g03*g04*g07*g08*gm5 + g01*g02*g04*g05*g07*g08*gm3 +
g02*g03*g04*g05*g07*g08*gm1 + g01*g02*g03*g04*g06*g07*gm8 + g01*g02*g03*g04*g06*g08*gm7 +
g01*g02*g03*g06*g07*g08*gm4 + g01*g03*g04*g06*g07*g08*gm2 + g01*g02*g03*g04*g06*g011*gm5 +
g01*g02*g03*g05*g06*g08*gm7 + g01*g02*g03*g06*g07*g08*gm5 + g01*g02*g05*g06*g07*g08*gm3 +
g02*g03*g05*g06*g07*g08*gm1 + g01*g02*g03*g04*g07*g08*gm8 + g01*g02*g04*g05*g06*g08*gm7 +
g01*g02*g04*g06*g07*g08*gm5 + g01*g02*g05*g06*g07*g08*gm4 + g01*g04*g05*g06*g07*g08*gm2 +
g01*g02*g03*g04*g05*g011*gm8 + g01*g02*g03*g04*g06*g011*gm7 + g01*g02*g03*g04*g08*g011*gm5 +
g01*g03*g04*g05*g06*g08*gm7 + g01*g03*g04*g06*g07*g08*gm5 + g01*g03*g05*g06*g07*g08*gm4 +
g01*g04*g05*g06*g07*g08*gm3 + g03*g04*g05*g06*g07*g08*gm1 + g02*g03*g04*g05*g06*g08*gm7 +
g02*g03*g04*g06*g07*g08*gm5 + g02*g03*g05*g06*g07*g08*gm4 + g02*g04*g05*g06*g07*g08*gm3 +
g03*g04*g05*g06*g07*g08*gm2 + g01*g02*g03*g04*g07*g011*gm8 + g01*g02*g03*g04*g08*g011*gm7 +
g01*g02*g03*g06*g08*g011*gm5 + g01*g02*g04*g05*g06*g011*gm7 + g01*g02*g04*g06*g07*g011*gm5 +
g01*g02*g03*g06*g08*g011*gm7 + g01*g02*g04*g05*g07*g011*gm8 + g01*g02*g04*g05*g08*g011*gm7 +
g01*g02*g04*g07*g08*g011*gm5 + g01*g03*g04*g06*g08*g011*gm5 + g01*g03*g05*g06*g08*g011*gm4 +
g02*g03*g04*g05*g06*g011*gm7 + g02*g03*g04*g06*g07*g011*gm5 + g02*g04*g05*g06*g07*g011*gm3 +
g01*g02*g05*g06*g08*g011*gm7 + g01*g02*g06*g07*g08*g011*gm5 + g01*g03*g04*g06*g08*g011*gm7 +
g01*g03*g06*g07*g08*g011*gm4 + g02*g03*g04*g05*g07*g011*gm8 + g02*g03*g04*g05*g08*g011*gm7 +
g02*g03*g04*g07*g08*g011*gm5 + g02*g04*g05*g07*g08*g011*gm3 + g01*g04*g05*g06*g08*g011*gm7 +
g01*g04*g06*g07*g08*g011*gm5 + g01*g05*g06*g07*g08*g011*gm4 + g02*g03*g05*g06*g08*g011*gm7 +
g02*g03*g06*g07*g08*g011*gm5 + g02*g05*g06*g07*g08*g011*gm3 + g03*g04*g05*g06*g08*g011*gm7 +
g03*g04*g06*g07*g08*g011*gm5 + g03*g05*g06*g07*g08*g011*gm4 + g04*g05*g06*g07*g08*g011*gm3 +
g01*g02*g03*g04*g06*gm5*gm7 + g01*g02*g04*g05*g06*gm3*gm7 + g01*g02*g04*g06*g07*gm3*gm5 +
g02*g03*g04*g05*g06*gm1*gm7 + g02*g03*g04*g06*g07*gm1*gm5 + g02*g04*g05*g06*g07*gm1*gm3 +
g01*g02*g03*g04*g06*gm5*gm8 + g01*g02*g03*g06*g08*gm4*gm5 + g01*g02*g04*g05*g06*gm3*gm8 +
g01*g03*g04*g06*g08*gm2*gm5 + g01*g03*g05*g06*g08*gm2*gm4 + g02*g03*g04*g05*g06*gm1*gm8 +
g01*g02*g03*g04*g05*gm7*gm8 + g01*g02*g03*g04*g07*gm5*gm8 + g01*g02*g03*g04*g08*gm5*gm7 +
g01*g02*g04*g05*g07*gm3*gm8 + g01*g02*g04*g05*g08*gm3*gm7 + g01*g02*g04*g07*g08*gm3*gm5 +
g02*g03*g04*g05*g07*gm1*gm8 + g02*g03*g04*g05*g08*gm1*gm7 + g02*g03*g04*g07*g08*gm1*gm5 +
g02*g04*g05*g07*g08*gm1*gm3 + g01*g02*g03*g04*g06*gm7*gm8 + g01*g02*g03*g06*g08*gm4*gm7 +
g01*g02*g04*g06*g07*gm3*gm8 + g01*g03*g04*g06*g08*gm2*gm7 + g01*g03*g06*g07*g08*gm2*gm4 +
g02*g03*g04*g06*g07*gm1*gm8 + g01*g02*g03*g06*g08*gm5*gm7 + g01*g02*g05*g06*g08*gm3*gm7 +
g01*g02*g06*g07*g08*gm3*gm5 + g02*g03*g05*g06*g08*gm1*gm7 + g02*g03*g06*g07*g08*gm1*gm5 +
g02*g05*g06*g07*g08*gm1*gm3 + g01*g02*g03*g04*g08*gm7*gm8 + g01*g02*g04*g06*g08*gm5*gm7 +
g01*g02*g04*g07*g08*gm3*gm8 + g01*g02*g05*g06*g08*gm4*gm7 + g01*g02*g06*g07*g08*gm4*gm5 +
g01*g04*g05*g06*g08*gm2*gm7 + g01*g04*g06*g07*g08*gm2*gm5 + g01*g05*g06*g07*g08*gm2*gm4 +
g02*g03*g04*g07*g08*gm1*gm8 + g01*g02*g03*g04*g011*gm5*gm8 + g01*g03*g04*g06*g08*gm5*gm7 +
MATLAB Solution Continued 1:
g01*g03*g05*g06*g08*gm4*gm7 + g01*g03*g06*g07*g08*gm4*gm5 + g01*g04*g05*g06*g08*gm3*gm7 +
g01*g04*g06*g07*g08*gm3*gm5 + g01*g05*g06*g07*g08*gm3*gm4 + g03*g04*g05*g06*g08*gm1*gm7 +
g03*g04*g06*g07*g08*gm1*gm5 + g03*g05*g06*g07*g08*gm1*gm4 + g04*g05*g06*g07*g08*gm1*gm3 +
g02*g03*g04*g06*g08*gm5*gm7 + g02*g03*g05*g06*g08*gm4*gm7 + g02*g03*g06*g07*g08*gm4*gm5 +
g02*g04*g05*g06*g08*gm3*gm7 + g02*g04*g06*g07*g08*gm3*gm5 + g02*g05*g06*g07*g08*gm3*gm4 +
g03*g04*g05*g06*g08*gm2*gm7 + g03*g04*g06*g07*g08*gm2*gm5 + g03*g05*g06*g07*g08*gm2*gm4 +
g04*g05*g06*g07*g08*gm2*gm3 + g01*g02*g03*g04*g011*gm7*gm8 + g01*g02*g04*g06*g011*gm5*gm7 +
g01*g02*g04*g05*g011*gm7*gm8 + g01*g02*g04*g07*g011*gm5*gm8 + g01*g02*g04*g08*g011*gm5*gm7 +
g01*g03*g06*g08*g011*gm4*gm5 + g02*g03*g04*g06*g011*gm5*gm7 + g02*g04*g05*g06*g011*gm3*gm7 +
g02*g04*g06*g07*g011*gm3*gm5 + g01*g02*g06*g08*g011*gm5*gm7 + g01*g03*g06*g08*g011*gm4*gm7 +
g02*g03*g04*g05*g011*gm7*gm8 + g02*g03*g04*g07*g011*gm5*gm8 + g02*g03*g04*g08*g011*gm5*gm7 +
g02*g04*g05*g07*g011*gm3*gm8 + g02*g04*g05*g08*g011*gm3*gm7 + g02*g04*g07*g08*g011*gm3*gm5 +
g01*g04*g06*g08*g011*gm5*gm7 + g01*g05*g06*g08*g011*gm4*gm7 + g01*g06*g07*g08*g011*gm4*gm5 +
g02*g03*g06*g08*g011*gm5*gm7 + g02*g05*g06*g08*g011*gm3*gm7 + g02*g06*g07*g08*g011*gm3*gm5 +
g03*g04*g06*g08*g011*gm5*gm7 + g03*g05*g06*g08*g011*gm4*gm7 + g03*g06*g07*g08*g011*gm4*gm5 +
g04*g05*g06*g08*g011*gm3*gm7 + g04*g06*g07*g08*g011*gm3*gm5 + g05*g06*g07*g08*g011*gm3*gm4 +
g01*g02*g04*g06*gm3*gm5*gm7 + g02*g03*g04*g06*gm1*gm5*gm7 + g02*g04*g05*g06*gm1*gm3*gm7 +
g02*g04*g06*g07*gm1*gm3*gm5 + g01*g02*g04*g06*gm3*gm5*gm8 + g01*g03*g06*g08*gm2*gm4*gm5 +
g02*g03*g04*g06*gm1*gm5*gm8 + g02*g04*g05*g06*gm1*gm3*gm8 + g01*g02*g03*g04*gm5*gm7*gm8 +
g01*g02*g04*g05*gm3*gm7*gm8 + g01*g02*g04*g07*gm3*gm5*gm8 + g01*g02*g04*g08*gm3*gm5*gm7 +
g02*g03*g04*g05*gm1*gm7*gm8 + g02*g03*g04*g07*gm1*gm5*gm8 + g02*g03*g04*g08*gm1*gm5*gm7 +
g02*g04*g05*g07*gm1*gm3*gm8 + g02*g04*g05*g08*gm1*gm3*gm7 + g02*g04*g07*g08*gm1*gm3*gm5 +
g01*g02*g04*g06*gm3*gm7*gm8 + g01*g03*g06*g08*gm2*gm4*gm7 + g02*g03*g04*g06*gm1*gm7*gm8 +
g02*g04*g06*g07*gm1*gm3*gm8 + g01*g02*g06*g08*gm3*gm5*gm7 + g02*g03*g06*g08*gm1*gm5*gm7 +
g02*g05*g06*g08*gm1*gm3*gm7 + g02*g06*g07*g08*gm1*gm3*gm5 + g01*g02*g04*g08*gm3*gm7*gm8 +
g01*g02*g06*g08*gm4*gm5*gm7 + g01*g04*g06*g08*gm2*gm5*gm7 + g01*g05*g06*g08*gm2*gm4*gm7 +
g01*g06*g07*g08*gm2*gm4*gm5 + g02*g03*g04*g08*gm1*gm7*gm8 + g02*g04*g07*g08*gm1*gm3*gm8 +
g01*g03*g06*g08*gm4*gm5*gm7 + g01*g04*g06*g08*gm3*gm5*gm7 + g01*g05*g06*g08*gm3*gm4*gm7 +
g01*g06*g07*g08*gm3*gm4*gm5 + g03*g04*g06*g08*gm1*gm5*gm7 + g03*g05*g06*g08*gm1*gm4*gm7 +
g03*g06*g07*g08*gm1*gm4*gm5 + g04*g05*g06*g08*gm1*gm3*gm7 + g04*g06*g07*g08*gm1*gm3*gm5 +
g05*g06*g07*g08*gm1*gm3*gm4 + g02*g03*g06*g08*gm4*gm5*gm7 + g02*g04*g06*g08*gm3*gm5*gm7 +
g02*g05*g06*g08*gm3*gm4*gm7 + g02*g06*g07*g08*gm3*gm4*gm5 + g03*g04*g06*g08*gm2*gm5*gm7 +
g03*g05*g06*g08*gm2*gm4*gm7 + g03*g06*g07*g08*gm2*gm4*gm5 + g04*g05*g06*g08*gm2*gm3*gm7 +
g04*g06*g07*g08*gm2*gm3*gm5 + g05*g06*g07*g08*gm2*gm3*gm4 + g01*g02*g04*g011*gm5*gm7*gm8 +
g02*g04*g06*g011*gm3*gm5*gm7 + g02*g03*g04*g011*gm5*gm7*gm8 + g02*g04*g05*g011*gm3*gm7*gm8 +
g02*g04*g07*g011*gm3*gm5*gm8 + g02*g04*g08*g011*gm3*gm5*gm7 + g01*g06*g08*g011*gm4*gm5*gm7 +
g02*g06*g08*g011*gm3*gm5*gm7 + g03*g06*g08*g011*gm4*gm5*gm7 + g04*g06*g08*g011*gm3*gm5*gm7 +
g05*g06*g08*g011*gm3*gm4*gm7 + g06*g07*g08*g011*gm3*gm4*gm5 + g02*g04*g06*gm1*gm3*gm5*gm7 +
g02*g04*g06*gm1*gm3*gm5*gm8 + g01*g02*g04*gm3*gm5*gm7*gm8 + g02*g03*g04*gm1*gm5*gm7*gm8 +
g02*g04*g05*gm1*gm3*gm7*gm8 + g02*g04*g07*gm1*gm3*gm5*gm8 + g02*g04*g08*gm1*gm3*gm5*gm7 +
g02*g04*g06*gm1*gm3*gm7*gm8 + g02*g06*g08*gm1*gm3*gm5*gm7 + g01*g06*g08*gm2*gm4*gm5*gm7 +
g02*g04*g08*gm1*gm3*gm7*gm8 + g01*g06*g08*gm3*gm4*gm5*gm7 + g03*g06*g08*gm1*gm4*gm5*gm7 +
g04*g06*g08*gm1*gm3*gm5*gm7 + g05*g06*g08*gm1*gm3*gm4*gm7 + g06*g07*g08*gm1*gm3*gm4*gm5 +
g02*g06*g08*gm3*gm4*gm5*gm7 + g03*g06*g08*gm2*gm4*gm5*gm7 + g04*g06*g08*gm2*gm3*gm5*gm7 +
g05*g06*g08*gm2*gm3*gm4*gm7 + g06*g07*g08*gm2*gm3*gm4*gm5 + g02*g04*g011*gm3*gm5*gm7*gm8 +
g06*g08*g011*gm3*gm4*gm5*gm7 + g02*g04*gm1*gm3*gm5*gm7*gm8 + g06*g08*gm1*gm3*gm4*gm5*gm7 +
g06*g08*gm2*gm3*gm4*gm5*gm7 + CL*g01*g02*g03*g04*g05*g06*s + CL*g01*g02*g03*g04*g05*g08*s +
CL*g01*g02*g03*g04*g06*g07*s + CL*g01*g02*g03*g05*g06*g07*s + CL*g01*g02*g03*g04*g07*g08*s +
CL*g01*g02*g04*g05*g06*g07*s + CL*g01*g02*g03*g05*g07*g08*s + CL*g01*g03*g04*g05*g06*g07*s +
CL*g01*g02*g04*g05*g07*g08*s + CL*g02*g03*g04*g05*g06*g07*s + CL*g01*g02*g03*g05*g06*g011*s +
CL*g01*g03*g04*g05*g07*g08*s + CL*g02*g03*g04*g05*g07*g08*s + CL*g01*g02*g03*g05*g08*g011*s +
CL*g01*g02*g03*g06*g07*g011*s + CL*g01*g03*g04*g05*g06*g011*s + CL*g01*g02*g03*g07*g08*g011*s +
CL*g01*g02*g05*g06*g07*g011*s + CL*g01*g03*g04*g05*g08*g011*s + CL*g01*g03*g04*g06*g07*g011*s +
CL*g01*g02*g05*g07*g08*g011*s + CL*g01*g03*g04*g07*g08*g011*s + CL*g01*g04*g05*g06*g07*g011*s +
CL*g02*g03*g05*g06*g07*g011*s + CL*g01*g04*g05*g07*g08*g011*s + CL*g02*g03*g05*g07*g08*g011*s +
CL*g03*g04*g05*g06*g07*g011*s + CL*g03*g04*g05*g07*g08*g011*s + CL*g01*g02*g03*g04*g06*gm5*s +
CL*g01*g02*g03*g05*g06*gm4*s + CL*g01*g03*g04*g05*g06*gm2*s + CL*g01*g02*g03*g04*g05*gm8*s +
CL*g01*g02*g03*g04*g06*gm7*s + CL*g01*g02*g03*g04*g08*gm5*s + CL*g01*g02*g03*g05*g08*gm4*s +
CL*g01*g02*g03*g06*g07*gm4*s + CL*g01*g03*g04*g05*g08*gm2*s + CL*g01*g03*g04*g06*g07*gm2*s +
CL*g01*g02*g03*g05*g06*gm7*s + CL*g01*g02*g03*g06*g07*gm5*s + CL*g01*g02*g05*g06*g07*gm3*s +
CL*g02*g03*g05*g06*g07*gm1*s + CL*g01*g02*g03*g04*g07*gm8*s + CL*g01*g02*g03*g04*g08*gm7*s +
CL*g01*g02*g03*g07*g08*gm4*s + CL*g01*g02*g04*g05*g06*gm7*s + CL*g01*g02*g04*g06*g07*gm5*s +
CL*g01*g02*g05*g06*g07*gm4*s + CL*g01*g03*ng04*g07*g08*gm2*s + CL*g01*g04*g05*g06*g07*gm2*s +
CL*g01*g02*g03*g05*g07*gm8*s + CL*g01*g02*g03*g05*g08*gm7*s + CL*g01*g02*g03*g07*g08*gm5*s +
CL*g01*g02*g05*g07*g08*gm3*s + CL*g01*g03*g04*g05*g06*gm7*s + CL*g01*g03*g04*g06*g07*gm5*s +
CL*g01*g03*g05*g06*g07*gm4*s + CL*g01*g04*g05*g06*g07*gm3*s + CL*g02*g03*g05*g07*g08*gm1*s +
CL*g03*g04*g05*g06*g07*gm1*s + CL*g01*g02*g04*g05*g07*gm8*s + CL*g01*g02*g04*g05*g08*gm7*s +
CL*g01*g02*g04*g07*g08*gm5*s + CL*g01*g02*g05*g07*g08*gm4*s + CL*g01*g04*g05*g07*g08*gm2*s +
CL*g02*g03*g04*g05*g06*gm7*s + CL*g02*g03*g04*g06*g07*gm5*s + CL*g02*g03*g05*g06*g07*gm4*s +
CL*g02*g04*g05*g06*g07*gm3*s + CL*g03*g04*g05*g06*g07*gm2*s + CL*g01*g02*g03*g06*g011*gm5*s +
CL*g01*g03*g04*g05*g07*gm8*s + CL*g01*g03*g04*g05*g08*gm7*s + CL*g01*g03*g04*g07*g08*gm5*s +
MATLAB Solution Continued 2:
CL*g01*g03*g05*g07*g08*gm4*s + CL*g01*g04*g05*g07*g08*gm3*s + CL*g03*g04*g05*g07*g08*gm1*s +
CL*g02*g03*g04*g05*g07*gm8*s + CL*g02*g03*g04*g05*g08*gm7*s + CL*g02*g03*g04*g07*g08*gm5*s +
CL*g02*g03*g05*g07*g08*gm4*s + CL*g02*g04*g05*g07*g08*gm3*s + CL*g03*g04*g05*g07*g08*gm2*s +
CL*g01*g02*g03*g05*g011*gm8*s + CL*g01*g02*g03*g06*g011*gm7*s + CL*g01*g02*g03*g08*g011*gm5*s +
CL*g01*g03*g04*g06*g011*gm5*s + CL*g01*g03*g05*g06*g011*gm4*s + CL*g01*g02*g03*g07*g011*gm8*s +
CL*g01*g02*g03*g08*g011*gm7*s + CL*g01*g02*g05*g06*g011*gm7*s + CL*g01*g02*g06*g07*g011*gm5*s +
CL*g01*g03*g04*g05*g011*gm8*s + CL*g01*g03*g04*g06*g011*gm7*s + CL*g01*g03*g04*g08*g011*gm5*s +
CL*g01*g03*g05*g08*g011*gm4*s + CL*g01*g03*g06*g07*g011*gm4*s + CL*g01*g02*g05*g07*g011*gm8*s +
CL*g01*g02*g05*g08*g011*gm7*s + CL*g01*g02*g07*g08*g011*gm5*s + CL*g01*g03*g04*g07*g011*gm8*s +
CL*g01*g03*g04*g08*g011*gm7*s + CL*g01*g03*g07*g08*g011*gm4*s + CL*g01*g04*g05*g06*g011*gm7*s +
CL*g01*g04*g06*g07*g011*gm5*s + CL*g01*g05*g06*g07*g011*gm4*s + CL*g02*g03*g05*g06*g011*gm7*s +
CL*g02*g03*g06*g07*g011*gm5*s + CL*g02*g05*g06*g07*g011*gm3*s + CL*g01*g04*g05*g07*g011*gm8*s +
CL*g01*g04*g05*g08*g011*gm7*s + CL*g01*g04*g07*g08*g011*gm5*s + CL*g01*g05*g07*g08*g011*gm4*s +
CL*g02*g03*g05*g07*g011*gm8*s + CL*g02*g03*g05*g08*g011*gm7*s + CL*g02*g03*g07*g08*g011*gm5*s +
CL*g02*g05*g07*g08*g011*gm3*s + CL*g03*g04*g05*g06*g011*gm7*s + CL*g03*g04*g06*g07*g011*gm5*s +
CL*g03*g05*g06*g07*g011*gm4*s + CL*g04*g05*g06*g07*g011*gm3*s + CL*g03*g04*g05*g07*g011*gm8*s +
CL*g03*g04*g05*g08*g011*gm7*s + CL*g03*g04*g07*g08*g011*gm5*s + CL*g03*g05*g07*g08*g011*gm4*s +
CL*g04*g05*g07*g08*g011*gm3*s + CL*g01*g02*g03*g06*gm4*gm5*s + CL*g01*g03*g04*g06*gm2*gm5*s +
CL*g01*g03*g05*g06*gm2*gm4*s + CL*g01*g02*g03*g04*gm5*gm8*s + CL*g01*g02*g03*g05*gm4*gm8*s +
CL*g01*g02*g03*g06*gm4*gm7*s + CL*g01*g02*g03*g08*gm4*gm5*s + CL*g01*g03*g04*g05*gm2*gm8*s +
CL*g01*g03*g04*g06*gm2*gm7*s + CL*g01*g03*g04*g08*gm2*gm5*s + CL*g01*g03*g05*g08*gm2*gm4*s +
CL*g01*g03*g06*g07*gm2*gm4*s + CL*g01*g02*g03*g06*gm5*gm7*s + CL*g01*g02*g05*g06*gm3*gm7*s +
CL*g01*g02*g06*g07*gm3*gm5*s + CL*g02*g03*g05*g06*gm1*gm7*s + CL*g02*g03*g06*g07*gm1*gm5*s +
CL*g02*g05*g06*g07*gm1*gm3*s + CL*g01*g02*g03*g04*gm7*gm8*s + CL*g01*g02*g03*g07*gm4*gm8*s +
CL*g01*g02*g03*g08*gm4*gm7*s + CL*g01*g02*g04*g06*gm5*gm7*s + CL*g01*g02*g05*g06*gm4*gm7*s +
CL*g01*g02*g06*g07*gm4*gm5*s + CL*g01*g03*g04*g07*gm2*gm8*s + CL*g01*g03*g04*g08*gm2*gm7*s +
CL*g01*g03*g07*g08*gm2*gm4*s + CL*g01*g04*g05*g06*gm2*gm7*s + CL*g01*g04*g06*g07*gm2*gm5*s +
CL*g01*g05*g06*g07*gm2*gm4*s + CL*g01*g02*g03*g05*gm7*gm8*s + CL*g01*g02*g03*g07*gm5*gm8*s +
CL*g01*g02*g03*g08*gm5*gm7*s + CL*g01*g02*g05*g07*gm3*gm8*s + CL*g01*g02*g05*g08*gm3*gm7*s +
CL*g01*g02*g07*g08*gm3*gm5*s + CL*g01*g03*g04*g06*gm5*gm7*s + CL*g01*g03*g05*g06*gm4*gm7*s +
CL*g01*g03*g06*g07*gm4*gm5*s + CL*g01*g04*g05*g06*gm3*gm7*s + CL*g01*g04*g06*g07*gm3*gm5*s +
CL*g01*g05*g06*g07*gm3*gm4*s + CL*g02*g03*g05*g07*gm1*gm8*s + CL*g02*g03*g05*g08*gm1*gm7*s +
CL*g02*g03*g07*g08*gm1*gm5*s + CL*g02*g05*g07*g08*gm1*gm3*s + CL*g03*g04*g05*g06*gm1*gm7*s +
CL*g03*g04*g06*g07*gm1*gm5*s + CL*g03*g05*g06*g07*gm1*gm4*s + CL*g04*g05*g06*g07*gm1*gm3*s +
CL*g01*g02*g04*g05*gm7*gm8*s + CL*g01*g02*g04*g07*gm5*gm8*s + CL*g01*g02*g04*g08*gm5*gm7*s +
CL*g01*g02*g05*g07*gm4*gm8*s + CL*g01*g02*g05*g08*gm4*gm7*s + CL*g01*g02*g07*g08*gm4*gm5*s +
CL*g01*g04*g05*g07*gm2*gm8*s + CL*g01*g04*g05*g08*gm2*gm7*s + CL*g01*g04*g07*g08*gm2*gm5*s +
CL*g01*g05*g07*g08*gm2*gm4*s + CL*g02*g03*g04*g06*gm5*gm7*s + CL*g02*g03*g05*g06*gm4*gm7*s +
CL*g02*g03*g06*g07*gm4*gm5*s + CL*g02*g04*g05*g06*gm3*gm7*s + CL*g02*g04*g06*g07*gm3*gm5*s +
CL*g02*g05*g06*g07*gm3*gm4*s + CL*g03*g04*g05*g06*gm2*gm7*s + CL*g03*g04*g06*g07*gm2*gm5*s +
CL*g03*g05*g06*g07*gm2*gm4*s + CL*g04*g05*g06*g07*gm2*gm3*s + CL*g01*g03*g04*g05*gm7*gm8*s +
CL*g01*g03*g04*g07*gm5*gm8*s + CL*g01*g03*g04*g08*gm5*gm7*s + CL*g01*g03*g05*g07*gm4*gm8*s +
CL*g01*g03*g05*g08*gm4*gm7*s + CL*g01*g03*g07*g08*gm4*gm5*s + CL*g01*g04*g05*g07*gm3*gm8*s +
CL*g01*g04*g05*g08*gm3*gm7*s + CL*g01*g04*g07*g08*gm3*gm5*s + CL*g01*g05*g07*g08*gm3*gm4*s +
CL*g03*g04*g05*g07*gm1*gm8*s + CL*g03*g04*g05*g08*gm1*gm7*s + CL*g03*g04*g07*g08*gm1*gm5*s +
CL*g03*g05*g07*g08*gm1*gm4*s + CL*g04*g05*g07*g08*gm1*gm3*s + CL*g02*g03*g04*g05*gm7*gm8*s +
CL*g02*g03*g04*g07*gm5*gm8*s + CL*g02*g03*g04*g08*gm5*gm7*s + CL*g02*g03*g05*g07*gm4*gm8*s +
CL*g02*g03*g05*g08*gm4*gm7*s + CL*g02*g03*g07*g08*gm4*gm5*s + CL*g02*g04*g05*g07*gm3*gm8*s +
CL*g02*g04*g05*g08*gm3*gm7*s + CL*g02*g04*g07*g08*gm3*gm5*s + CL*g02*g05*g07*g08*gm3*gm4*s +
CL*g03*g04*g05*g07*gm2*gm8*s + CL*g03*g04*g05*g08*gm2*gm7*s + CL*g03*g04*g07*g08*gm2*gm5*s +
CL*g03*g05*g07*g08*gm2*gm4*s + CL*g04*g05*g07*g08*gm2*gm3*s + CL*g01*g02*g03*g011*gm5*gm8*s +
CL*g01*g03*g06*g011*gm4*gm5*s + CL*g01*g02*g03*g011*gm7*gm8*s + CL*g01*g02*g06*g011*gm5*gm7*s +
CL*g01*g03*g04*g011*gm5*gm8*s + CL*g01*g03*g05*g011*gm4*gm8*s + CL*g01*g03*g06*g011*gm4*gm7*s +
CL*g01*g03*g08*g011*gm4*gm5*s + CL*g01*g02*g05*g011*gm7*gm8*s + CL*g01*g02*g07*g011*gm5*gm8*s +
CL*g01*g02*g08*g011*gm5*gm7*s + CL*g01*g03*g04*g011*gm7*gm8*s + CL*g01*g03*g07*g011*gm4*gm8*s +
CL*g01*g03*g08*g011*gm4*gm7*s + CL*g01*g04*g06*g011*gm5*gm7*s + CL*g01*g05*g06*g011*gm4*gm7*s +
CL*g01*g06*g07*g011*gm4*gm5*s + CL*g02*g03*g06*g011*gm5*gm7*s + CL*g02*g05*g06*g011*gm3*gm7*s +
CL*g02*g06*g07*g011*gm3*gm5*s + CL*g01*g04*g05*g011*gm7*gm8*s + CL*g01*g04*g07*g011*gm5*gm8*s +
CL*g01*g04*g08*g011*gm5*gm7*s + CL*g01*g05*g07*g011*gm4*gm8*s + CL*g01*g05*g08*g011*gm4*gm7*s +
CL*g01*g07*g08*g011*gm4*gm5*s + CL*g02*g03*g05*g011*gm7*gm8*s + CL*g02*g03*g07*g011*gm5*gm8*s +
CL*g02*g03*g08*g011*gm5*gm7*s + CL*g02*g05*g07*g011*gm3*gm8*s + CL*g02*g05*g08*g011*gm3*gm7*s +
CL*g02*g07*g08*g011*gm3*gm5*s + CL*g03*g04*g06*g011*gm5*gm7*s + CL*g03*g05*g06*g011*gm4*gm7*s +
CL*g03*g06*g07*g011*gm4*gm5*s + CL*g04*g05*g06*g011*gm3*gm7*s + CL*g04*g06*g07*g011*gm3*gm5*s +
CL*g05*g06*g07*g011*gm3*gm4*s + CL*g03*g04*g05*g011*gm7*gm8*s + CL*g03*g04*g07*g011*gm5*gm8*s +
CL*g03*g04*g08*g011*gm5*gm7*s + CL*g03*g05*g07*g011*gm4*gm8*s + CL*g03*g05*g08*g011*gm4*gm7*s +
CL*g03*g07*g08*g011*gm4*gm5*s + CL*g04*g05*g07*g011*gm3*gm8*s + CL*g04*g05*g08*g011*gm3*gm7*s +
CL*g04*g07*g08*g011*gm3*gm5*s + CL*g05*g07*g08*g011*gm3*gm4*s + CL*g01*g03*g06*gm2*gm4*gm5*s +
CL*g01*g02*g03*gm4*gm5*gm8*s + CL*g01*g03*g04*gm2*gm5*gm8*s + CL*g01*g03*g05*gm2*gm4*gm8*s +
CL*g01*g03*g06*gm2*gm4*gm7*s + CL*g01*g03*g08*gm2*gm4*gm5*s + CL*g01*g02*g06*gm3*gm5*gm7*s +
CL*g02*g03*g06*gm1*gm5*gm7*s + CL*g02*g05*g06*gm1*gm3*gm7*s + CL*g02*g06*g07*gm1*gm3*gm5*s +
CL*g01*g02*g03*gm4*gm7*gm8*s + CL*g01*g02*g06*gm4*gm5*gm7*s + CL*g01*g03*g04*gm2*gm7*gm8*s +
MATLAB Solution Continued 3:
CL*g01*g03*g07*gm2*gm4*gm8*s + CL*g01*g03*g08*gm2*gm4*gm7*s + CL*g01*g04*g06*gm2*gm5*gm7*s +
CL*g01*g05*g06*gm2*gm4*gm7*s + CL*g01*g06*g07*gm2*gm4*gm5*s + CL*g01*g02*g03*gm5*gm7*gm8*s +
CL*g01*g02*g05*gm3*gm7*gm8*s + CL*g01*g02*g07*gm3*gm5*gm8*s + CL*g01*g02*g08*gm3*gm5*gm7*s +
CL*g01*g03*g06*gm4*gm5*gm7*s + CL*g01*g04*g06*gm3*gm5*gm7*s + CL*g01*g05*g06*gm3*gm4*gm7*s +
CL*g01*g06*g07*gm3*gm4*gm5*s + CL*g02*g03*g05*gm1*gm7*gm8*s + CL*g02*g03*g07*gm1*gm5*gm8*s +
CL*g02*g03*g08*gm1*gm5*gm7*s + CL*g02*g05*g07*gm1*gm3*gm8*s + CL*g02*g05*g08*gm1*gm3*gm7*s +
CL*g02*g07*g08*gm1*gm3*gm5*s + CL*g03*g04*g06*gm1*gm5*gm7*s + CL*g03*g05*g06*gm1*gm4*gm7*s +
CL*g03*g06*g07*gm1*gm4*gm5*s + CL*g04*g05*g06*gm1*gm3*gm7*s + CL*g04*g06*g07*gm1*gm3*gm5*s +
CL*g05*g06*g07*gm1*gm3*gm4*s + CL*g01*g02*g04*gm5*gm7*gm8*s + CL*g01*g02*g05*gm4*gm7*gm8*s +
CL*g01*g02*g07*gm4*gm5*gm8*s + CL*g01*g02*g08*gm4*gm5*gm7*s + CL*g01*g04*g05*gm2*gm7*gm8*s +
CL*g01*g04*g07*gm2*gm5*gm8*s + CL*g01*g04*g08*gm2*gm5*gm7*s + CL*g01*g05*g07*gm2*gm4*gm8*s +
CL*g01*g05*g08*gm2*gm4*gm7*s + CL*g01*g07*g08*gm2*gm4*gm5*s + CL*g02*g03*g06*gm4*gm5*gm7*s +
CL*g02*g04*g06*gm3*gm5*gm7*s + CL*g02*g05*g06*gm3*gm4*gm7*s + CL*g02*g06*g07*gm3*gm4*gm5*s +
CL*g03*g04*g06*gm2*gm5*gm7*s + CL*g03*g05*g06*gm2*gm4*gm7*s + CL*g03*g06*g07*gm2*gm4*gm5*s +
CL*g04*g05*g06*gm2*gm3*gm7*s + CL*g04*g06*g07*gm2*gm3*gm5*s + CL*g05*g06*g07*gm2*gm3*gm4*s +
CL*g01*g03*g04*gm5*gm7*gm8*s + CL*g01*g03*g05*gm4*gm7*gm8*s + CL*g01*g03*g07*gm4*gm5*gm8*s +
CL*g01*g03*g08*gm4*gm5*gm7*s + CL*g01*g04*g05*gm3*gm7*gm8*s + CL*g01*g04*g07*gm3*gm5*gm8*s +
CL*g01*g04*g08*gm3*gm5*gm7*s + CL*g01*g05*g07*gm3*gm4*gm8*s + CL*g01*g05*g08*gm3*gm4*gm7*s +
CL*g01*g07*g08*gm3*gm4*gm5*s + CL*g03*g04*g05*gm1*gm7*gm8*s + CL*g03*g04*g07*gm1*gm5*gm8*s +
CL*g03*g04*g08*gm1*gm5*gm7*s + CL*g03*g05*g07*gm1*gm4*gm8*s + CL*g03*g05*g08*gm1*gm4*gm7*s +
CL*g03*g07*g08*gm1*gm4*gm5*s + CL*g04*g05*g07*gm1*gm3*gm8*s + CL*g04*g05*g08*gm1*gm3*gm7*s +
CL*g04*g07*g08*gm1*gm3*gm5*s + CL*g05*g07*g08*gm1*gm3*gm4*s + CL*g02*g03*g04*gm5*gm7*gm8*s +
CL*g02*g03*g05*gm4*gm7*gm8*s + CL*g02*g03*g07*gm4*gm5*gm8*s + CL*g02*g03*g08*gm4*gm5*gm7*s +
CL*g02*g04*g05*gm3*gm7*gm8*s + CL*g02*g04*g07*gm3*gm5*gm8*s + CL*g02*g04*g08*gm3*gm5*gm7*s +
CL*g02*g05*g07*gm3*gm4*gm8*s + CL*g02*g05*g08*gm3*gm4*gm7*s + CL*g02*g07*g08*gm3*gm4*gm5*s +
CL*g03*g04*g05*gm2*gm7*gm8*s + CL*g03*g04*g07*gm2*gm5*gm8*s + CL*g03*g04*g08*gm2*gm5*gm7*s +
CL*g03*g05*g07*gm2*gm4*gm8*s + CL*g03*g05*g08*gm2*gm4*gm7*s + CL*g03*g07*g08*gm2*gm4*gm5*s +
CL*g04*g05*g07*gm2*gm3*gm8*s + CL*g04*g05*g08*gm2*gm3*gm7*s + CL*g04*g07*g08*gm2*gm3*gm5*s +
CL*g05*g07*g08*gm2*gm3*gm4*s + CL*g01*g03*g011*gm4*gm5*gm8*s + CL*g01*g02*g011*gm5*gm7*gm8*s +
CL*g01*g03*g011*gm4*gm7*gm8*s + CL*g01*g06*g011*gm4*gm5*gm7*s + CL*g02*g06*g011*gm3*gm5*gm7*s +
CL*g01*g04*g011*gm5*gm7*gm8*s + CL*g01*g05*g011*gm4*gm7*gm8*s + CL*g01*g07*g011*gm4*gm5*gm8*s +
CL*g01*g08*g011*gm4*gm5*gm7*s + CL*g02*g03*g011*gm5*gm7*gm8*s + CL*g02*g05*g011*gm3*gm7*gm8*s +
CL*g02*g07*g011*gm3*gm5*gm8*s + CL*g02*g08*g011*gm3*gm5*gm7*s + CL*g03*g06*g011*gm4*gm5*gm7*s +
CL*g04*g06*g011*gm3*gm5*gm7*s + CL*g05*g06*g011*gm3*gm4*gm7*s + CL*g06*g07*g011*gm3*gm4*gm5*s +
CL*g03*g04*g011*gm5*gm7*gm8*s + CL*g03*g05*g011*gm4*gm7*gm8*s + CL*g03*g07*g011*gm4*gm5*gm8*s +
CL*g03*g08*g011*gm4*gm5*gm7*s + CL*g04*g05*g011*gm3*gm7*gm8*s + CL*g04*g07*g011*gm3*gm5*gm8*s +
CL*g04*g08*g011*gm3*gm5*gm7*s + CL*g05*g07*g011*gm3*gm4*gm8*s + CL*g05*g08*g011*gm3*gm4*gm7*s +
CL*g07*g08*g011*gm3*gm4*gm5*s + CL*g01*g03*gm2*gm4*gm5*gm8*s + CL*g02*g06*gm1*gm3*gm5*gm7*s +
CL*g01*g03*gm2*gm4*gm7*gm8*s + CL*g01*g06*gm2*gm4*gm5*gm7*s + CL*g01*g02*gm3*gm5*gm7*gm8*s +
CL*g01*g06*gm3*gm4*gm5*gm7*s + CL*g02*g03*gm1*gm5*gm7*gm8*s + CL*g02*g05*gm1*gm3*gm7*gm8*s +
CL*g02*g07*gm1*gm3*gm5*gm8*s + CL*g02*g08*gm1*gm3*gm5*gm7*s + CL*g03*g06*gm1*gm4*gm5*gm7*s +
CL*g04*g06*gm1*gm3*gm5*gm7*s + CL*g05*g06*gm1*gm3*gm4*gm7*s + CL*g06*g07*gm1*gm3*gm4*gm5*s +
CL*g01*g02*gm4*gm5*gm7*gm8*s + CL*g01*g04*gm2*gm5*gm7*gm8*s + CL*g01*g05*gm2*gm4*gm7*gm8*s +
CL*g01*g07*gm2*gm4*gm5*gm8*s + CL*g01*g08*gm2*gm4*gm5*gm7*s + CL*g02*g06*gm3*gm4*gm5*gm7*s +
CL*g03*g06*gm2*gm4*gm5*gm7*s + CL*g04*g06*gm2*gm3*gm5*gm7*s + CL*g05*g06*gm2*gm3*gm4*gm7*s +
CL*g06*g07*gm2*gm3*gm4*gm5*s + CL*g01*g03*gm4*gm5*gm7*gm8*s + CL*g01*g04*gm3*gm5*gm7*gm8*s +
CL*g01*g05*gm3*gm4*gm7*gm8*s + CL*g01*g07*gm3*gm4*gm5*gm8*s + CL*g01*g08*gm3*gm4*gm5*gm7*s +
CL*g03*g04*gm1*gm5*gm7*gm8*s + CL*g03*g05*gm1*gm4*gm7*gm8*s + CL*g03*g07*gm1*gm4*gm5*gm8*s +
CL*g03*g08*gm1*gm4*gm5*gm7*s + CL*g04*g05*gm1*gm3*gm7*gm8*s + CL*g04*g07*gm1*gm3*gm5*gm8*s +
CL*g04*g08*gm1*gm3*gm5*gm7*s + CL*g05*g07*gm1*gm3*gm4*gm8*s + CL*g05*g08*gm1*gm3*gm4*gm7*s +
CL*g07*g08*gm1*gm3*gm4*gm5*s + CL*g02*g03*gm4*gm5*gm7*gm8*s + CL*g02*g04*gm3*gm5*gm7*gm8*s +
CL*g02*g05*gm3*gm4*gm7*gm8*s + CL*g02*g07*gm3*gm4*gm5*gm8*s + CL*g02*g08*gm3*gm4*gm5*gm7*s +
CL*g03*g04*gm2*gm5*gm7*gm8*s + CL*g03*g05*gm2*gm4*gm7*gm8*s + CL*g03*g07*gm2*gm4*gm5*gm8*s +
CL*g03*g08*gm2*gm4*gm5*gm7*s + CL*g04*g05*gm2*gm3*gm7*gm8*s + CL*g04*g07*gm2*gm3*gm5*gm8*s +
CL*g04*g08*gm2*gm3*gm5*gm7*s + CL*g05*g07*gm2*gm3*gm4*gm8*s + CL*g05*g08*gm2*gm3*gm4*gm7*s +
CL*g07*g08*gm2*gm3*gm4*gm5*s + CL*g01*g011*gm4*gm5*gm7*gm8*s + CL*g02*g011*gm3*gm5*gm7*gm8*s +
CL*g06*g011*gm3*gm4*gm5*gm7*s + CL*g03*g011*gm4*gm5*gm7*gm8*s + CL*g04*g011*gm3*gm5*gm7*gm8*s +
CL*g05*g011*gm3*gm4*gm7*gm8*s + CL*g07*g011*gm3*gm4*gm5*gm8*s + CL*g08*g011*gm3*gm4*gm5*gm7*s +
CL*g02*gm1*gm3*gm5*gm7*gm8*s + CL*g06*gm1*gm3*gm4*gm5*gm7*s + CL*g01*gm2*gm4*gm5*gm7*gm8*s +
CL*g06*gm2*gm3*gm4*gm5*gm7*s + CL*g01*gm3*gm4*gm5*gm7*gm8*s + CL*g03*gm1*gm4*gm5*gm7*gm8*s +
CL*g04*gm1*gm3*gm5*gm7*gm8*s + CL*g05*gm1*gm3*gm4*gm7*gm8*s + CL*g07*gm1*gm3*gm4*gm5*gm8*s +
CL*g08*gm1*gm3*gm4*gm5*gm7*s + CL*g02*gm3*gm4*gm5*gm7*gm8*s + CL*g03*gm2*gm4*gm5*gm7*gm8*s +
CL*g04*gm2*gm3*gm5*gm7*gm8*s + CL*g05*gm2*gm3*gm4*gm7*gm8*s + CL*g07*gm2*gm3*gm4*gm5*gm8*s +
CL*g08*gm2*gm3*gm4*gm5*gm7*s + CL*g011*gm3*gm4*gm5*gm7*gm8*s + CL*gm1*gm3*gm4*gm5*gm7*gm8*s +
CL*gm2*gm3*gm4*gm5*gm7*gm8*s))*Vinn + (Vinp*g02*g03*g04*g07*gm1*gm8^2 +
Vinp*g02*g03*g07*g011*gm1*gm8^2 + Vinp*g03*g04*g07*g011*gm1*gm8^2 +
Vinp*g02*g03*g04*gm1*gm7*gm8^2 + Vinp*g02*g03*g07*gm1*gm4*gm8^2 + Vinp*g02*g04*g07*gm1*gm3*gm8^2
+ Vinp*g03*g04*g07*gm1*gm2*gm8^2 + Vinp*g02*g03*g011*gm1*gm7*gm8^2 +
Vinp*g02*g07*g011*gm1*gm3*gm8^2 + Vinp*g03*g04*g011*gm1*gm7*gm8^2 +
Vinp*g03*g07*g011*gm1*gm4*gm8^2 + Vinp*g04*g07*g011*gm1*gm3*gm8^2 +
Vinp*g02*g03*gm1*gm4*gm7*gm8^2 + Vinp*g02*g04*gm1*gm3*gm7*gm8^2 + Vinp*g02*g07*gm1*gm3*gm4*gm8^2
MATLAB Solution Continued 4:
+ Vinp*g03*g04*gm1*gm2*gm7*gm8^2 + Vinp*g03*g07*gm1*gm2*gm4*gm8^2 +
Vinp*g04*g07*gm1*gm2*gm3*gm8^2 + Vinp*g02*g011*gm1*gm3*gm7*gm8^2 +
Vinp*g03*g011*gm1*gm4*gm7*gm8^2 + Vinp*g04*g011*gm1*gm3*gm7*gm8^2 +
Vinp*g07*g011*gm1*gm3*gm4*gm8^2 + Vinp*g02*gm1*gm3*gm4*gm7*gm8^2 +
Vinp*g03*gm1*gm2*gm4*gm7*gm8^2 + Vinp*g04*gm1*gm2*gm3*gm7*gm8^2 + Vinp*g07*gm1*gm2*gm3*gm4*gm8^2
+ Vinp*g011*gm1*gm3*gm4*gm7*gm8^2 + Vinp*gm1*gm2*gm3*gm4*gm7*gm8^2 +
Vinp*g02*g03*g04*g05*g06*g07*gm1 + Vinp*g02*g03*g04*g05*g07*g08*gm1 +
Vinp*g02*g03*g04*g05*g06*gm1*gm7 + Vinp*g02*g03*g04*g06*g07*gm1*gm5 +
Vinp*g02*g03*g05*g06*g07*gm1*gm4 + Vinp*g02*g04*g05*g06*g07*gm1*gm3 +
Vinp*g03*g04*g05*g06*g07*gm1*gm2 + Vinp*g02*g03*g04*g05*g06*gm1*gm8 +
Vinp*g02*g03*g04*g05*g07*gm1*gm8 + Vinp*g02*g03*g04*g05*g08*gm1*gm7 +
Vinp*g02*g03*g04*g07*g08*gm1*gm5 + Vinp*g02*g03*g05*g07*g08*gm1*gm4 +
Vinp*g02*g04*g05*g07*g08*gm1*gm3 + Vinp*g03*g04*g05*g07*g08*gm1*gm2 +
Vinp*g02*g03*g04*g06*g07*gm1*gm8 + Vinp*g02*g03*g04*g07*g08*gm1*gm8 +
Vinp*g02*g03*g05*g06*g011*gm1*gm8 + Vinp*g02*g03*g06*g07*g011*gm1*gm8 +
Vinp*g03*g04*g05*g06*g011*gm1*gm8 + Vinp*g02*g03*g07*g08*g011*gm1*gm8 +
Vinp*g03*g04*g06*g07*g011*gm1*gm8 + Vinp*g03*g04*g07*g08*g011*gm1*gm8 +
Vinp*g02*g03*g04*g06*gm1*gm5*gm7 + Vinp*g02*g03*g05*g06*gm1*gm4*gm7 +
Vinp*g02*g03*g06*g07*gm1*gm4*gm5 + Vinp*g02*g04*g05*g06*gm1*gm3*gm7 +
Vinp*g02*g04*g06*g07*gm1*gm3*gm5 + Vinp*g02*g05*g06*g07*gm1*gm3*gm4 +
Vinp*g03*g04*g05*g06*gm1*gm2*gm7 + Vinp*g03*g04*g06*g07*gm1*gm2*gm5 +
Vinp*g03*g05*g06*g07*gm1*gm2*gm4 + Vinp*g04*g05*g06*g07*gm1*gm2*gm3 +
Vinp*g02*g03*g04*g06*gm1*gm5*gm8 + Vinp*g02*g03*g05*g06*gm1*gm4*gm8 +
Vinp*g02*g04*g05*g06*gm1*gm3*gm8 + Vinp*g03*g04*g05*g06*gm1*gm2*gm8 +
Vinp*g02*g03*g04*g05*gm1*gm7*gm8 + Vinp*g02*g03*g04*g07*gm1*gm5*gm8 +
Vinp*g02*g03*g04*g08*gm1*gm5*gm7 + Vinp*g02*g03*g05*g07*gm1*gm4*gm8 +
Vinp*g02*g03*g05*g08*gm1*gm4*gm7 + Vinp*g02*g03*g07*g08*gm1*gm4*gm5 +
Vinp*g02*g04*g05*g07*gm1*gm3*gm8 + Vinp*g02*g04*g05*g08*gm1*gm3*gm7 +
Vinp*g02*g04*g07*g08*gm1*gm3*gm5 + Vinp*g02*g05*g07*g08*gm1*gm3*gm4 +
Vinp*g03*g04*g05*g07*gm1*gm2*gm8 + Vinp*g03*g04*g05*g08*gm1*gm2*gm7 +
Vinp*g03*g04*g07*g08*gm1*gm2*gm5 + Vinp*g03*g05*g07*g08*gm1*gm2*gm4 +
Vinp*g04*g05*g07*g08*gm1*gm2*gm3 + Vinp*g02*g03*g04*g06*gm1*gm7*gm8 +
Vinp*g02*g03*g06*g07*gm1*gm4*gm8 + Vinp*g02*g04*g06*g07*gm1*gm3*gm8 +
Vinp*g03*g04*g06*g07*gm1*gm2*gm8 + Vinp*g02*g03*g04*g08*gm1*gm7*gm8 +
Vinp*g02*g03*g07*g08*gm1*gm4*gm8 + Vinp*g02*g04*g07*g08*gm1*gm3*gm8 +
Vinp*g03*g04*g07*g08*gm1*gm2*gm8 + Vinp*g02*g03*g06*g011*gm1*gm5*gm8 +
Vinp*g02*g05*g06*g011*gm1*gm3*gm8 + Vinp*g02*g03*g06*g011*gm1*gm7*gm8 +
Vinp*g02*g06*g07*g011*gm1*gm3*gm8 + Vinp*g03*g04*g06*g011*gm1*gm5*gm8 +
Vinp*g03*g05*g06*g011*gm1*gm4*gm8 + Vinp*g04*g05*g06*g011*gm1*gm3*gm8 +
Vinp*g02*g03*g08*g011*gm1*gm7*gm8 + Vinp*g02*g07*g08*g011*gm1*gm3*gm8 +
Vinp*g03*g04*g06*g011*gm1*gm7*gm8 + Vinp*g03*g06*g07*g011*gm1*gm4*gm8 +
Vinp*g04*g06*g07*g011*gm1*gm3*gm8 + Vinp*g03*g04*g08*g011*gm1*gm7*gm8 +
Vinp*g03*g07*g08*g011*gm1*gm4*gm8 + Vinp*g04*g07*g08*g011*gm1*gm3*gm8 +
Vinp*g02*g03*g06*gm1*gm4*gm5*gm7 + Vinp*g02*g04*g06*gm1*gm3*gm5*gm7 +
Vinp*g02*g05*g06*gm1*gm3*gm4*gm7 + Vinp*g02*g06*g07*gm1*gm3*gm4*gm5 +
Vinp*g03*g04*g06*gm1*gm2*gm5*gm7 + Vinp*g03*g05*g06*gm1*gm2*gm4*gm7 +
Vinp*g03*g06*g07*gm1*gm2*gm4*gm5 + Vinp*g04*g05*g06*gm1*gm2*gm3*gm7 +
Vinp*g04*g06*g07*gm1*gm2*gm3*gm5 + Vinp*g05*g06*g07*gm1*gm2*gm3*gm4 +
Vinp*g02*g03*g06*gm1*gm4*gm5*gm8 + Vinp*g02*g04*g06*gm1*gm3*gm5*gm8 +
Vinp*g02*g05*g06*gm1*gm3*gm4*gm8 + Vinp*g03*g04*g06*gm1*gm2*gm5*gm8 +
Vinp*g03*g05*g06*gm1*gm2*gm4*gm8 + Vinp*g04*g05*g06*gm1*gm2*gm3*gm8 +
Vinp*g02*g03*g04*gm1*gm5*gm7*gm8 + Vinp*g02*g03*g05*gm1*gm4*gm7*gm8 +
Vinp*g02*g03*g07*gm1*gm4*gm5*gm8 + Vinp*g02*g03*g08*gm1*gm4*gm5*gm7 +
Vinp*g02*g04*g05*gm1*gm3*gm7*gm8 + Vinp*g02*g04*g07*gm1*gm3*gm5*gm8 +
Vinp*g02*g04*g08*gm1*gm3*gm5*gm7 + Vinp*g02*g05*g07*gm1*gm3*gm4*gm8 +
Vinp*g02*g05*g08*gm1*gm3*gm4*gm7 + Vinp*g02*g07*g08*gm1*gm3*gm4*gm5 +
Vinp*g03*g04*g05*gm1*gm2*gm7*gm8 + Vinp*g03*g04*g07*gm1*gm2*gm5*gm8 +
Vinp*g03*g04*g08*gm1*gm2*gm5*gm7 + Vinp*g03*g05*g07*gm1*gm2*gm4*gm8 +
Vinp*g03*g05*g08*gm1*gm2*gm4*gm7 + Vinp*g03*g07*g08*gm1*gm2*gm4*gm5 +
Vinp*g04*g05*g07*gm1*gm2*gm3*gm8 + Vinp*g04*g05*g08*gm1*gm2*gm3*gm7 +
Vinp*g04*g07*g08*gm1*gm2*gm3*gm5 + Vinp*g05*g07*g08*gm1*gm2*gm3*gm4 +
Vinp*g02*g03*g06*gm1*gm4*gm7*gm8 + Vinp*g02*g04*g06*gm1*gm3*gm7*gm8 +
Vinp*g02*g06*g07*gm1*gm3*gm4*gm8 + Vinp*g03*g04*g06*gm1*gm2*gm7*gm8 +
Vinp*g03*g06*g07*gm1*gm2*gm4*gm8 + Vinp*g04*g06*g07*gm1*gm2*gm3*gm8 +
Vinp*g02*g03*g08*gm1*gm4*gm7*gm8 + Vinp*g02*g04*g08*gm1*gm3*gm7*gm8 +
Vinp*g02*g07*g08*gm1*gm3*gm4*gm8 + Vinp*g03*g04*g08*gm1*gm2*gm7*gm8 +
Vinp*g03*g07*g08*gm1*gm2*gm4*gm8 + Vinp*g04*g07*g08*gm1*gm2*gm3*gm8 +
Vinp*g02*g06*g011*gm1*gm3*gm5*gm8 + Vinp*g02*g06*g011*gm1*gm3*gm7*gm8 +
Vinp*g03*g06*g011*gm1*gm4*gm5*gm8 + Vinp*g04*g06*g011*gm1*gm3*gm5*gm8 +
Vinp*g05*g06*g011*gm1*gm3*gm4*gm8 + Vinp*g02*g08*g011*gm1*gm3*gm7*gm8 +
Vinp*g03*g06*g011*gm1*gm4*gm7*gm8 + Vinp*g04*g06*g011*gm1*gm3*gm7*gm8 +
MATLAB Solution Continued 5:
Vinp*g06*g07*g011*gm1*gm3*gm4*gm8 + Vinp*g03*g08*g011*gm1*gm4*gm7*gm8 +
Vinp*g04*g08*g011*gm1*gm3*gm7*gm8 + Vinp*g07*g08*g011*gm1*gm3*gm4*gm8 +
Vinp*g02*g06*gm1*gm3*gm4*gm5*gm7 + Vinp*g03*g06*gm1*gm2*gm4*gm5*gm7 +
Vinp*g04*g06*gm1*gm2*gm3*gm5*gm7 + Vinp*g05*g06*gm1*gm2*gm3*gm4*gm7 +
Vinp*g06*g07*gm1*gm2*gm3*gm4*gm5 + Vinp*g02*g06*gm1*gm3*gm4*gm5*gm8 +
Vinp*g03*g06*gm1*gm2*gm4*gm5*gm8 + Vinp*g04*g06*gm1*gm2*gm3*gm5*gm8 +
Vinp*g05*g06*gm1*gm2*gm3*gm4*gm8 + Vinp*g02*g03*gm1*gm4*gm5*gm7*gm8 +
Vinp*g02*g04*gm1*gm3*gm5*gm7*gm8 + Vinp*g02*g05*gm1*gm3*gm4*gm7*gm8 +
Vinp*g02*g07*gm1*gm3*gm4*gm5*gm8 + Vinp*g02*g08*gm1*gm3*gm4*gm5*gm7 +
Vinp*g03*g04*gm1*gm2*gm5*gm7*gm8 + Vinp*g03*g05*gm1*gm2*gm4*gm7*gm8 +
Vinp*g03*g07*gm1*gm2*gm4*gm5*gm8 + Vinp*g03*g08*gm1*gm2*gm4*gm5*gm7 +
Vinp*g04*g05*gm1*gm2*gm3*gm7*gm8 + Vinp*g04*g07*gm1*gm2*gm3*gm5*gm8 +
Vinp*g04*g08*gm1*gm2*gm3*gm5*gm7 + Vinp*g05*g07*gm1*gm2*gm3*gm4*gm8 +
Vinp*g05*g08*gm1*gm2*gm3*gm4*gm7 + Vinp*g07*g08*gm1*gm2*gm3*gm4*gm5 +
Vinp*g02*g06*gm1*gm3*gm4*gm7*gm8 + Vinp*g03*g06*gm1*gm2*gm4*gm7*gm8 +
Vinp*g04*g06*gm1*gm2*gm3*gm7*gm8 + Vinp*g06*g07*gm1*gm2*gm3*gm4*gm8 +
Vinp*g02*g08*gm1*gm3*gm4*gm7*gm8 + Vinp*g03*g08*gm1*gm2*gm4*gm7*gm8 +
Vinp*g04*g08*gm1*gm2*gm3*gm7*gm8 + Vinp*g07*g08*gm1*gm2*gm3*gm4*gm8 +
Vinp*g06*g011*gm1*gm3*gm4*gm5*gm8 + Vinp*g06*g011*gm1*gm3*gm4*gm7*gm8 +
Vinp*g08*g011*gm1*gm3*gm4*gm7*gm8 + Vinp*g06*gm1*gm2*gm3*gm4*gm5*gm7 +
Vinp*g06*gm1*gm2*gm3*gm4*gm5*gm8 + Vinp*g02*gm1*gm3*gm4*gm5*gm7*gm8 +
Vinp*g03*gm1*gm2*gm4*gm5*gm7*gm8 + Vinp*g04*gm1*gm2*gm3*gm5*gm7*gm8 +
Vinp*g05*gm1*gm2*gm3*gm4*gm7*gm8 + Vinp*g07*gm1*gm2*gm3*gm4*gm5*gm8 +
Vinp*g08*gm1*gm2*gm3*gm4*gm5*gm7 + Vinp*g06*gm1*gm2*gm3*gm4*gm7*gm8 +
Vinp*g08*gm1*gm2*gm3*gm4*gm7*gm8 + Vinp*gm1*gm2*gm3*gm4*gm5*gm7*gm8)
/
(g01*g02*g03*g04*g07*gm8^2 + g01*g02*g03*g04*gm7*gm8^2 + g01*g02*g04*g07*gm3*gm8^2 +
g02*g03*g04*g07*gm1*gm8^2 + g01*g02*g04*gm3*gm7*gm8^2 + g02*g03*g04*gm1*gm7*gm8^2 +
g02*g04*g07*gm1*gm3*gm8^2 + g02*g04*gm1*gm3*gm7*gm8^2 + g01*g02*g03*g04*g05*g06*g07 +
g01*g02*g03*g04*g05*g06*g08 + g01*g02*g03*g04*g05*g07*g08 + g01*g02*g03*g04*g06*g07*g08 +
g01*g02*g03*g04*g05*g06*g011 + g01*g02*g03*g05*g06*g07*g08 + g01*g02*g04*g05*g06*g07*g08 +
g01*g02*g03*g04*g05*g08*g011 + g01*g02*g03*g04*g06*g07*g011 + g01*g03*g04*g05*g06*g07*g08 +
g02*g03*g04*g05*g06*g07*g08 + g01*g02*g03*g04*g07*g08*g011 + g01*g02*g03*g05*g06*g08*g011 +
g01*g02*g04*g05*g06*g07*g011 + g01*g02*g03*g06*g07*g08*g011 + g01*g02*g04*g05*g07*g08*g011 +
g01*g03*g04*g05*g06*g08*g011 + g02*g03*g04*g05*g06*g07*g011 + g01*g02*g05*g06*g07*g08*g011 +
g01*g03*g04*g06*g07*g08*g011 + g02*g03*g04*g05*g07*g08*g011 + g01*g04*g05*g06*g07*g08*g011 +
g02*g03*g05*g06*g07*g08*g011 + g03*g04*g05*g06*g07*g08*g011 + g01*g02*g03*g04*g05*g06*gm7 +
g01*g02*g03*g04*g06*g07*gm5 + g01*g02*g04*g05*g06*g07*gm3 + g02*g03*g04*g05*g06*g07*gm1 +
g01*g02*g03*g04*g05*g06*gm8 + g01*g02*g03*g04*g06*g08*gm5 + g01*g02*g03*g05*g06*g08*gm4 +
g01*g03*g04*g05*g06*g08*gm2 + g01*g02*g03*g04*g05*g07*gm8 + g01*g02*g03*g04*g05*g08*gm7 +
g01*g02*g03*g04*g07*g08*gm5 + g01*g02*g04*g05*g07*g08*gm3 + g02*g03*g04*g05*g07*g08*gm1 +
g01*g02*g03*g04*g06*g07*gm8 + g01*g02*g03*g04*g06*g08*gm7 + g01*g02*g03*g06*g07*g08*gm4 +
g01*g03*g04*g06*g07*g08*gm2 + g01*g02*g03*g04*g06*g011*gm5 + g01*g02*g03*g05*g06*g08*gm7 +
g01*g02*g03*g06*g07*g08*gm5 + g01*g02*g05*g06*g07*g08*gm3 + g02*g03*g05*g06*g07*g08*gm1 +
g01*g02*g03*g04*g07*g08*gm8 + g01*g02*g04*g05*g06*g08*gm7 + g01*g02*g04*g06*g07*g08*gm5 +
g01*g02*g05*g06*g07*g08*gm4 + g01*g04*g05*g06*g07*g08*gm2 + g01*g02*g03*g04*g05*g011*gm8 +
g01*g02*g03*g04*g06*g011*gm7 + g01*g02*g03*g04*g08*g011*gm5 + g01*g03*g04*g05*g06*g08*gm7 +
g01*g03*g04*g06*g07*g08*gm5 + g01*g03*g05*g06*g07*g08*gm4 + g01*g04*g05*g06*g07*g08*gm3 +
g03*g04*g05*g06*g07*g08*gm1 + g02*g03*g04*g05*g06*g08*gm7 + g02*g03*g04*g06*g07*g08*gm5 +
g02*g03*g05*g06*g07*g08*gm4 + g02*g04*g05*g06*g07*g08*gm3 + g03*g04*g05*g06*g07*g08*gm2 +
g01*g02*g03*g04*g07*g011*gm8 + g01*g02*g03*g04*g08*g011*gm7 + g01*g02*g03*g06*g08*g011*gm5 +
g01*g02*g04*g05*g06*g011*gm7 + g01*g02*g04*g06*g07*g011*gm5 + g01*g02*g03*g06*g08*g011*gm7 +
g01*g02*g04*g05*g07*g011*gm8 + g01*g02*g04*g05*g08*g011*gm7 + g01*g02*g04*g07*g08*g011*gm5 +
g01*g03*g04*g06*g08*g011*gm5 + g01*g03*g05*g06*g08*g011*gm4 + g02*g03*g04*g05*g06*g011*gm7 +
g02*g03*g04*g06*g07*g011*gm5 + g02*g04*g05*g06*g07*g011*gm3 + g01*g02*g05*g06*g08*g011*gm7 +
g01*g02*g06*g07*g08*g011*gm5 + g01*g03*g04*g06*g08*g011*gm7 + g01*g03*g06*g07*g08*g011*gm4 +
g02*g03*g04*g05*g07*g011*gm8 + g02*g03*g04*g05*g08*g011*gm7 + g02*g03*g04*g07*g08*g011*gm5 +
g02*g04*g05*g07*g08*g011*gm3 + g01*g04*g05*g06*g08*g011*gm7 + g01*g04*g06*g07*g08*g011*gm5 +
g01*g05*g06*g07*g08*g011*gm4 + g02*g03*g05*g06*g08*g011*gm7 + g02*g03*g06*g07*g08*g011*gm5 +
g02*g05*g06*g07*g08*g011*gm3 + g03*g04*g05*g06*g08*g011*gm7 + g03*g04*g06*g07*g08*g011*gm5 +
g03*g05*g06*g07*g08*g011*gm4 + g04*g05*g06*g07*g08*g011*gm3 + g01*g02*g03*g04*g06*gm5*gm7 +
g01*g02*g04*g05*g06*gm3*gm7 + g01*g02*g04*g06*g07*gm3*gm5 + g02*g03*g04*g05*g06*gm1*gm7 +
g02*g03*g04*g06*g07*gm1*gm5 + g02*g04*g05*g06*g07*gm1*gm3 + g01*g02*g03*g04*g06*gm5*gm8 +
g01*g02*g03*g06*g08*gm4*gm5 + g01*g02*g04*g05*g06*gm3*gm8 + g01*g03*g04*g06*g08*gm2*gm5 +
g01*g03*g05*g06*g08*gm2*gm4 + g02*g03*g04*g05*g06*gm1*gm8 + g01*g02*g03*g04*g05*gm7*gm8 +
g01*g02*g03*g04*g07*gm5*gm8 + g01*g02*g03*g04*g08*gm5*gm7 + g01*g02*g04*g05*g07*gm3*gm8 +
g01*g02*g04*g05*g08*gm3*gm7 + g01*g02*g04*g07*g08*gm3*gm5 + g02*g03*g04*g05*g07*gm1*gm8 +
g02*g03*g04*g05*g08*gm1*gm7 + g02*g03*g04*g07*g08*gm1*gm5 + g02*g04*g05*g07*g08*gm1*gm3 +
g01*g02*g03*g04*g06*gm7*gm8 + g01*g02*g03*g06*g08*gm4*gm7 + g01*g02*g04*g06*g07*gm3*gm8 +
MATLAB Solution Continued 6:
g01*g03*g04*g06*g08*gm2*gm7 + g01*g03*g06*g07*g08*gm2*gm4 + g02*g03*g04*g06*g07*gm1*gm8 +
g01*g02*g03*g06*g08*gm5*gm7 + g01*g02*g05*g06*g08*gm3*gm7 + g01*g02*g06*g07*g08*gm3*gm5 +
g02*g03*g05*g06*g08*gm1*gm7 + g02*g03*g06*g07*g08*gm1*gm5 + g02*g05*g06*g07*g08*gm1*gm3 +
g01*g02*g03*g04*g08*gm7*gm8 + g01*g02*g04*g06*g08*gm5*gm7 + g01*g02*g04*g07*g08*gm3*gm8 +
g01*g02*g05*g06*g08*gm4*gm7 + g01*g02*g06*g07*g08*gm4*gm5 + g01*g04*g05*g06*g08*gm2*gm7 +
g01*g04*g06*g07*g08*gm2*gm5 + g01*g05*g06*g07*g08*gm2*gm4 + g02*g03*g04*g07*g08*gm1*gm8 +
g01*g02*g03*g04*g011*gm5*gm8 + g01*g03*g04*g06*g08*gm5*gm7 + g01*g03*g05*g06*g08*gm4*gm7 +
g01*g03*g06*g07*g08*gm4*gm5 + g01*g04*g05*g06*g08*gm3*gm7 + g01*g04*g06*g07*g08*gm3*gm5 +
g01*g05*g06*g07*g08*gm3*gm4 + g03*g04*g05*g06*g08*gm1*gm7 + g03*g04*g06*g07*g08*gm1*gm5 +
g03*g05*g06*g07*g08*gm1*gm4 + g04*g05*g06*g07*g08*gm1*gm3 + g02*g03*g04*g06*g08*gm5*gm7 +
g02*g03*g05*g06*g08*gm4*gm7 + g02*g03*g06*g07*g08*gm4*gm5 + g02*g04*g05*g06*g08*gm3*gm7 +
g02*g04*g06*g07*g08*gm3*gm5 + g02*g05*g06*g07*g08*gm3*gm4 + g03*g04*g05*g06*g08*gm2*gm7 +
g03*g04*g06*g07*g08*gm2*gm5 + g03*g05*g06*g07*g08*gm2*gm4 + g04*g05*g06*g07*g08*gm2*gm3 +
g01*g02*g03*g04*g011*gm7*gm8 + g01*g02*g04*g06*g011*gm5*gm7 + g01*g02*g04*g05*g011*gm7*gm8 +
g01*g02*g04*g07*g011*gm5*gm8 + g01*g02*g04*g08*g011*gm5*gm7 + g01*g03*g06*g08*g011*gm4*gm5 +
g02*g03*g04*g06*g011*gm5*gm7 + g02*g04*g05*g06*g011*gm3*gm7 + g02*g04*g06*g07*g011*gm3*gm5 +
g01*g02*g06*g08*g011*gm5*gm7 + g01*g03*g06*g08*g011*gm4*gm7 + g02*g03*g04*g05*g011*gm7*gm8 +
g02*g03*g04*g07*g011*gm5*gm8 + g02*g03*g04*g08*g011*gm5*gm7 + g02*g04*g05*g07*g011*gm3*gm8 +
g02*g04*g05*g08*g011*gm3*gm7 + g02*g04*g07*g08*g011*gm3*gm5 + g01*g04*g06*g08*g011*gm5*gm7 +
g01*g05*g06*g08*g011*gm4*gm7 + g01*g06*g07*g08*g011*gm4*gm5 + g02*g03*g06*g08*g011*gm5*gm7 +
g02*g05*g06*g08*g011*gm3*gm7 + g02*g06*g07*g08*g011*gm3*gm5 + g03*g04*g06*g08*g011*gm5*gm7 +
g03*g05*g06*g08*g011*gm4*gm7 + g03*g06*g07*g08*g011*gm4*gm5 + g04*g05*g06*g08*g011*gm3*gm7 +
g04*g06*g07*g08*g011*gm3*gm5 + g05*g06*g07*g08*g011*gm3*gm4 + g01*g02*g04*g06*gm3*gm5*gm7 +
g02*g03*g04*g06*gm1*gm5*gm7 + g02*g04*g05*g06*gm1*gm3*gm7 + g02*g04*g06*g07*gm1*gm3*gm5 +
g01*g02*g04*g06*gm3*gm5*gm8 + g01*g03*g06*g08*gm2*gm4*gm5 + g02*g03*g04*g06*gm1*gm5*gm8 +
g02*g04*g05*g06*gm1*gm3*gm8 + g01*g02*g03*g04*gm5*gm7*gm8 + g01*g02*g04*g05*gm3*gm7*gm8 +
g01*g02*g04*g07*gm3*gm5*gm8 + g01*g02*g04*g08*gm3*gm5*gm7 + g02*g03*g04*g05*gm1*gm7*gm8 +
g02*g03*g04*g07*gm1*gm5*gm8 + g02*g03*g04*g08*gm1*gm5*gm7 + g02*g04*g05*g07*gm1*gm3*gm8 +
g02*g04*g05*g08*gm1*gm3*gm7 + g02*g04*g07*g08*gm1*gm3*gm5 + g01*g02*g04*g06*gm3*gm7*gm8 +
g01*g03*g06*g08*gm2*gm4*gm7 + g02*g03*g04*g06*gm1*gm7*gm8 + g02*g04*g06*g07*gm1*gm3*gm8 +
g01*g02*g06*g08*gm3*gm5*gm7 + g02*g03*g06*g08*gm1*gm5*gm7 + g02*g05*g06*g08*gm1*gm3*gm7 +
g02*g06*g07*g08*gm1*gm3*gm5 + g01*g02*g04*g08*gm3*gm7*gm8 + g01*g02*g06*g08*gm4*gm5*gm7 +
g01*g04*g06*g08*gm2*gm5*gm7 + g01*g05*g06*g08*gm2*gm4*gm7 + g01*g06*g07*g08*gm2*gm4*gm5 +
g02*g03*g04*g08*gm1*gm7*gm8 + g02*g04*g07*g08*gm1*gm3*gm8 + g01*g03*g06*g08*gm4*gm5*gm7 +
g01*g04*g06*g08*gm3*gm5*gm7 + g01*g05*g06*g08*gm3*gm4*gm7 + g01*g06*g07*g08*gm3*gm4*gm5 +
g03*g04*g06*g08*gm1*gm5*gm7 + g03*g05*g06*g08*gm1*gm4*gm7 + g03*g06*g07*g08*gm1*gm4*gm5 +
g04*g05*g06*g08*gm1*gm3*gm7 + g04*g06*g07*g08*gm1*gm3*gm5 + g05*g06*g07*g08*gm1*gm3*gm4 +
g02*g03*g06*g08*gm4*gm5*gm7 + g02*g04*g06*g08*gm3*gm5*gm7 + g02*g05*g06*g08*gm3*gm4*gm7 +
g02*g06*g07*g08*gm3*gm4*gm5 + g03*g04*g06*g08*gm2*gm5*gm7 + g03*g05*g06*g08*gm2*gm4*gm7 +
g03*g06*g07*g08*gm2*gm4*gm5 + g04*g05*g06*g08*gm2*gm3*gm7 + g04*g06*g07*g08*gm2*gm3*gm5 +
g05*g06*g07*g08*gm2*gm3*gm4 + g01*g02*g04*g011*gm5*gm7*gm8 + g02*g04*g06*g011*gm3*gm5*gm7 +
g02*g03*g04*g011*gm5*gm7*gm8 + g02*g04*g05*g011*gm3*gm7*gm8 + g02*g04*g07*g011*gm3*gm5*gm8 +
g02*g04*g08*g011*gm3*gm5*gm7 + g01*g06*g08*g011*gm4*gm5*gm7 + g02*g06*g08*g011*gm3*gm5*gm7 +
g03*g06*g08*g011*gm4*gm5*gm7 + g04*g06*g08*g011*gm3*gm5*gm7 + g05*g06*g08*g011*gm3*gm4*gm7 +
g06*g07*g08*g011*gm3*gm4*gm5 + g02*g04*g06*gm1*gm3*gm5*gm7 + g02*g04*g06*gm1*gm3*gm5*gm8 +
g01*g02*g04*gm3*gm5*gm7*gm8 + g02*g03*g04*gm1*gm5*gm7*gm8 + g02*g04*g05*gm1*gm3*gm7*gm8 +
g02*g04*g07*gm1*gm3*gm5*gm8 + g02*g04*g08*gm1*gm3*gm5*gm7 + g02*g04*g06*gm1*gm3*gm7*gm8 +
g02*g06*g08*gm1*gm3*gm5*gm7 + g01*g06*g08*gm2*gm4*gm5*gm7 + g02*g04*g08*gm1*gm3*gm7*gm8 +
g01*g06*g08*gm3*gm4*gm5*gm7 + g03*g06*g08*gm1*gm4*gm5*gm7 + g04*g06*g08*gm1*gm3*gm5*gm7 +
g05*g06*g08*gm1*gm3*gm4*gm7 + g06*g07*g08*gm1*gm3*gm4*gm5 + g02*g06*g08*gm3*gm4*gm5*gm7 +
g03*g06*g08*gm2*gm4*gm5*gm7 + g04*g06*g08*gm2*gm3*gm5*gm7 + g05*g06*g08*gm2*gm3*gm4*gm7 +
g06*g07*g08*gm2*gm3*gm4*gm5 + g02*g04*g011*gm3*gm5*gm7*gm8 + g06*g08*g011*gm3*gm4*gm5*gm7 +
g02*g04*gm1*gm3*gm5*gm7*gm8 + g06*g08*gm1*gm3*gm4*gm5*gm7 + g06*g08*gm2*gm3*gm4*gm5*gm7 +
CL*g01*g02*g03*g04*g05*g06*s + CL*g01*g02*g03*g04*g05*g08*s + CL*g01*g02*g03*g04*g06*g07*s +
CL*g01*g02*g03*g05*g06*g07*s + CL*g01*g02*g03*g04*g07*g08*s + CL*g01*g02*g04*g05*g06*g07*s +
CL*g01*g02*g03*g05*g07*g08*s + CL*g01*g03*g04*g05*g06*g07*s + CL*g01*g02*g04*g05*g07*g08*s +
CL*g02*g03*g04*g05*g06*g07*s + CL*g01*g02*g03*g05*g06*g011*s + CL*g01*g03*g04*g05*g07*g08*s +
CL*g02*g03*g04*g05*g07*g08*s + CL*g01*g02*g03*g05*g08*g011*s + CL*g01*g02*g03*g06*g07*g011*s +
CL*g01*g03*g04*g05*g06*g011*s + CL*g01*g02*g03*g07*g08*g011*s + CL*g01*g02*g05*g06*g07*g011*s +
CL*g01*g03*g04*g05*g08*g011*s + CL*g01*g03*g04*g06*g07*g011*s + CL*g01*g02*g05*g07*g08*g011*s +
CL*g01*g03*g04*g07*g08*g011*s + CL*g01*g04*g05*g06*g07*g011*s + CL*g02*g03*g05*g06*g07*g011*s +
CL*g01*g04*g05*g07*g08*g011*s + CL*g02*g03*g05*g07*g08*g011*s + CL*g03*g04*g05*g06*g07*g011*s +
CL*g03*g04*g05*g07*g08*g011*s + CL*g01*g02*g03*g04*g06*gm5*s + CL*g01*g02*g03*g05*g06*gm4*s +
CL*g01*g03*g04*g05*g06*gm2*s + CL*g01*g02*g03*g04*g05*gm8*s + CL*g01*g02*g03*g04*g06*gm7*s +
CL*g01*g02*g03*g04*g08*gm5*s + CL*g01*g02*g03*g05*g08*gm4*s + CL*g01*g02*g03*g06*g07*gm4*s +
CL*g01*g03*g04*g05*g08*gm2*s + CL*g01*g03*g04*g06*g07*gm2*s + CL*g01*g02*g03*g05*g06*gm7*s +
CL*g01*g02*g03*g06*g07*gm5*s + CL*g01*g02*g05*g06*g07*gm3*s + CL*g02*g03*g05*g06*g07*gm1*s +
CL*g01*g02*g03*g04*g07*gm8*s + CL*g01*g02*g03*g04*g08*gm7*s + CL*g01*g02*g03*g07*g08*gm4*s +
CL*g01*g02*g04*g05*g06*gm7*s + CL*g01*g02*g04*g06*g07*gm5*s + CL*g01*g02*g05*g06*g07*gm4*s +
CL*g01*g03*g04*g07*g08*gm2*s + CL*g01*g04*g05*g06*g07*gm2*s + CL*g01*g02*g03*g05*g07*gm8*s +
CL*g01*g02*g03*g05*g08*gm7*s + CL*g01*g02*g03*g07*g08*gm5*s + CL*g01*g02*g05*g07*g08*gm3*s +
MATLAB Solution Continued 7:
CL*g01*g03*g04*g05*g06*gm7*s + CL*g01*g03*g04*g06*g07*gm5*s + CL*g01*g03*g05*g06*g07*gm4*s +
CL*g01*g04*g05*g06*g07*gm3*s + CL*g02*g03*g05*g07*g08*gm1*s + CL*g03*g04*g05*g06*g07*gm1*s +
CL*g01*g02*g04*g05*g07*gm8*s + CL*g01*g02*g04*g05*g08*gm7*s + CL*g01*g02*g04*g07*g08*gm5*s +
CL*g01*g02*g05*g07*g08*gm4*s + CL*g01*g04*g05*g07*g08*gm2*s + CL*g02*g03*g04*g05*g06*gm7*s +
CL*g02*g03*g04*g06*g07*gm5*s + CL*g02*g03*g05*g06*g07*gm4*s + CL*g02*g04*g05*g06*g07*gm3*s +
CL*g03*g04*g05*g06*g07*gm2*s + CL*g01*g02*g03*g06*g011*gm5*s + CL*g01*g03*g04*g05*g07*gm8*s +
CL*g01*g03*g04*g05*g08*gm7*s + CL*g01*g03*g04*g07*g08*gm5*s + CL*g01*g03*g05*g07*g08*gm4*s +
CL*g01*g04*g05*g07*g08*gm3*s + CL*g03*g04*g05*g07*g08*gm1*s + CL*g02*g03*g04*g05*g07*gm8*s +
CL*g02*g03*g04*g05*g08*gm7*s + CL*g02*g03*g04*g07*g08*gm5*s + CL*g02*g03*g05*g07*g08*gm4*s +
CL*g02*g04*g05*g07*g08*gm3*s + CL*g03*g04*g05*g07*g08*gm2*s + CL*g01*g02*g03*g05*g011*gm8*s +
CL*g01*g02*g03*g06*g011*gm7*s + CL*g01*g02*g03*g08*g011*gm5*s + CL*g01*g03*g04*g06*g011*gm5*s +
CL*g01*g03*g05*g06*g011*gm4*s + CL*g01*g02*g03*g07*g011*gm8*s + CL*g01*g02*g03*g08*g011*gm7*s +
CL*g01*g02*g05*g06*g011*gm7*s + CL*g01*g02*g06*g07*g011*gm5*s + CL*g01*g03*g04*g05*g011*gm8*s +
CL*g01*g03*g04*g06*g011*gm7*s + CL*g01*g03*g04*g08*g011*gm5*s + CL*g01*g03*g05*g08*g011*gm4*s +
CL*g01*g03*g06*g07*g011*gm4*s + CL*g01*g02*g05*g07*g011*gm8*s + CL*g01*g02*g05*g08*g011*gm7*s +
CL*g01*g02*g07*g08*g011*gm5*s + CL*g01*g03*g04*g07*g011*gm8*s + CL*g01*g03*g04*g08*g011*gm7*s +
CL*g01*g03*g07*g08*g011*gm4*s + CL*g01*g04*g05*g06*g011*gm7*s + CL*g01*g04*g06*g07*g011*gm5*s +
CL*g01*g05*g06*g07*g011*gm4*s + CL*g02*g03*g05*g06*g011*gm7*s + CL*g02*g03*g06*g07*g011*gm5*s +
CL*g02*g05*g06*g07*g011*gm3*s + CL*g01*g04*g05*g07*g011*gm8*s + CL*g01*g04*g05*g08*g011*gm7*s +
CL*g01*g04*g07*g08*g011*gm5*s + CL*g01*g05*g07*g08*g011*gm4*s + CL*g02*g03*g05*g07*g011*gm8*s +
CL*g02*g03*g05*g08*g011*gm7*s + CL*g02*g03*g07*g08*g011*gm5*s + CL*g02*g05*g07*g08*g011*gm3*s +
CL*g03*g04*g05*g06*g011*gm7*s + CL*g03*g04*g06*g07*g011*gm5*s + CL*g03*g05*g06*g07*g011*gm4*s +
CL*g04*g05*g06*g07*g011*gm3*s + CL*g03*g04*g05*g07*g011*gm8*s + CL*g03*g04*g05*g08*g011*gm7*s +
CL*g03*g04*g07*g08*g011*gm5*s + CL*g03*g05*g07*g08*g011*gm4*s + CL*g04*g05*g07*g08*g011*gm3*s +
CL*g01*g02*g03*g06*gm4*gm5*s + CL*g01*g03*g04*g06*gm2*gm5*s + CL*g01*g03*g05*g06*gm2*gm4*s +
CL*g01*g02*g03*g04*gm5*gm8*s + CL*g01*g02*g03*g05*gm4*gm8*s + CL*g01*g02*g03*g06*gm4*gm7*s +
CL*g01*g02*g03*g08*gm4*gm5*s + CL*g01*g03*g04*g05*gm2*gm8*s + CL*g01*g03*g04*g06*gm2*gm7*s +
CL*g01*g03*g04*g08*gm2*gm5*s + CL*g01*g03*g05*g08*gm2*gm4*s + CL*g01*g03*g06*g07*gm2*gm4*s +
CL*g01*g02*g03*g06*gm5*gm7*s + CL*g01*g02*g05*g06*gm3*gm7*s + CL*g01*g02*g06*g07*gm3*gm5*s +
CL*g02*g03*g05*g06*gm1*gm7*s + CL*g02*g03*g06*g07*gm1*gm5*s + CL*g02*g05*g06*g07*gm1*gm3*s +
CL*g01*g02*g03*g04*gm7*gm8*s + CL*g01*g02*g03*g07*gm4*gm8*s + CL*g01*g02*g03*g08*gm4*gm7*s +
CL*g01*g02*g04*g06*gm5*gm7*s + CL*g01*g02*g05*g06*gm4*gm7*s + CL*g01*g02*g06*g07*gm4*gm5*s +
CL*g01*g03*g04*g07*gm2*gm8*s + CL*g01*g03*g04*g08*gm2*gm7*s + CL*g01*g03*g07*g08*gm2*gm4*s +
CL*g01*g04*g05*g06*gm2*gm7*s + CL*g01*g04*g06*g07*gm2*gm5*s + CL*g01*g05*g06*g07*gm2*gm4*s +
CL*g01*g02*g03*g05*gm7*gm8*s + CL*g01*g02*g03*g07*gm5*gm8*s + CL*g01*g02*g03*g08*gm5*gm7*s +
CL*g01*g02*g05*g07*gm3*gm8*s + CL*g01*g02*g05*g08*gm3*gm7*s + CL*g01*g02*g07*g08*gm3*gm5*s +
CL*g01*g03*g04*g06*gm5*gm7*s + CL*g01*g03*g05*g06*gm4*gm7*s + CL*g01*g03*g06*g07*gm4*gm5*s +
CL*g01*g04*g05*g06*gm3*gm7*s + CL*g01*g04*g06*g07*gm3*gm5*s + CL*g01*g05*g06*g07*gm3*gm4*s +
CL*g02*g03*g05*g07*gm1*gm8*s + CL*g02*g03*g05*g08*gm1*gm7*s + CL*g02*g03*g07*g08*gm1*gm5*s +
CL*g02*g05*g07*g08*gm1*gm3*s + CL*g03*g04*g05*g06*gm1*gm7*s + CL*g03*g04*g06*g07*gm1*gm5*s +
CL*g03*g05*g06*g07*gm1*gm4*s + CL*g04*g05*g06*g07*gm1*gm3*s + CL*g01*g02*g04*g05*gm7*gm8*s +
CL*g01*g02*g04*g07*gm5*gm8*s + CL*g01*g02*g04*g08*gm5*gm7*s + CL*g01*g02*g05*g07*gm4*gm8*s +
CL*g01*g02*g05*g08*gm4*gm7*s + CL*g01*g02*g07*g08*gm4*gm5*s + CL*g01*g04*g05*g07*gm2*gm8*s +
CL*g01*g04*g05*g08*gm2*gm7*s + CL*g01*g04*g07*g08*gm2*gm5*s + CL*g01*g05*g07*g08*gm2*gm4*s +
CL*g02*g03*g04*g06*gm5*gm7*s + CL*g02*g03*g05*g06*gm4*gm7*s + CL*g02*g03*g06*g07*gm4*gm5*s +
CL*g02*g04*g05*g06*gm3*gm7*s + CL*g02*g04*g06*g07*gm3*gm5*s + CL*g02*g05*g06*g07*gm3*gm4*s +
CL*g03*g04*g05*g06*gm2*gm7*s + CL*g03*g04*g06*g07*gm2*gm5*s + CL*g03*g05*g06*g07*gm2*gm4*s +
CL*g04*g05*g06*g07*gm2*gm3*s + CL*g01*g03*g04*g05*gm7*gm8*s + CL*g01*g03*g04*g07*gm5*gm8*s +
CL*g01*g03*g04*g08*gm5*gm7*s + CL*g01*g03*g05*g07*gm4*gm8*s + CL*g01*g03*g05*g08*gm4*gm7*s +
CL*g01*g03*g07*g08*gm4*gm5*s + CL*g01*g04*g05*g07*gm3*gm8*s + CL*g01*g04*g05*g08*gm3*gm7*s +
CL*g01*g04*g07*g08*gm3*gm5*s + CL*g01*g05*g07*g08*gm3*gm4*s + CL*g03*g04*g05*g07*gm1*gm8*s +
CL*g03*g04*g05*g08*gm1*gm7*s + CL*g03*g04*g07*g08*gm1*gm5*s + CL*g03*g05*g07*g08*gm1*gm4*s +
CL*g04*g05*g07*g08*gm1*gm3*s + CL*g02*g03*g04*g05*gm7*gm8*s + CL*g02*g03*g04*g07*gm5*gm8*s +
CL*g02*g03*g04*g08*gm5*gm7*s + CL*g02*g03*g05*g07*gm4*gm8*s + CL*g02*g03*g05*g08*gm4*gm7*s +
CL*g02*g03*g07*g08*gm4*gm5*s + CL*g02*g04*g05*g07*gm3*gm8*s + CL*g02*g04*g05*g08*gm3*gm7*s +
CL*g02*g04*g07*g08*gm3*gm5*s + CL*g02*g05*g07*g08*gm3*gm4*s + CL*g03*g04*g05*g07*gm2*gm8*s +
CL*g03*g04*g05*g08*gm2*gm7*s + CL*g03*g04*g07*g08*gm2*gm5*s + CL*g03*g05*g07*g08*gm2*gm4*s +
CL*g04*g05*g07*g08*gm2*gm3*s + CL*g01*g02*g03*g011*gm5*gm8*s + CL*g01*g03*g06*g011*gm4*gm5*s +
CL*g01*g02*g03*g011*gm7*gm8*s + CL*g01*g02*g06*g011*gm5*gm7*s + CL*g01*g03*g04*g011*gm5*gm8*s +
CL*g01*g03*g05*g011*gm4*gm8*s + CL*g01*g03*g06*g011*gm4*gm7*s + CL*g01*g03*g08*g011*gm4*gm5*s +
CL*g01*g02*g05*g011*gm7*gm8*s + CL*g01*g02*g07*g011*gm5*gm8*s + CL*g01*g02*g08*g011*gm5*gm7*s +
CL*g01*g03*g04*g011*gm7*gm8*s + CL*g01*g03*g07*g011*gm4*gm8*s + CL*g01*g03*g08*g011*gm4*gm7*s +
CL*g01*g04*g06*g011*gm5*gm7*s + CL*g01*g05*g06*g011*gm4*gm7*s + CL*g01*g06*g07*g011*gm4*gm5*s +
CL*g02*g03*g06*g011*gm5*gm7*s + CL*g02*g05*g06*g011*gm3*gm7*s + CL*g02*g06*g07*g011*gm3*gm5*s +
CL*g01*g04*g05*g011*gm7*gm8*s + CL*g01*g04*g07*g011*gm5*gm8*s + CL*g01*g04*g08*g011*gm5*gm7*s +
CL*g01*g05*g07*g011*gm4*gm8*s + CL*g01*g05*g08*g011*gm4*gm7*s + CL*g01*g07*g08*g011*gm4*gm5*s +
CL*g02*g03*g05*g011*gm7*gm8*s + CL*g02*g03*g07*g011*gm5*gm8*s + CL*g02*g03*g08*g011*gm5*gm7*s +
CL*g02*g05*g07*g011*gm3*gm8*s + CL*g02*g05*g08*g011*gm3*gm7*s + CL*g02*g07*g08*g011*gm3*gm5*s +
CL*g03*g04*g06*g011*gm5*gm7*s + CL*g03*g05*g06*g011*gm4*gm7*s + CL*g03*g06*g07*g011*gm4*gm5*s +
CL*g04*g05*g06*g011*gm3*gm7*s + CL*g04*g06*g07*g011*gm3*gm5*s + CL*g05*g06*g07*g011*gm3*gm4*s +
CL*g03*g04*g05*g011*gm7*gm8*s + CL*g03*g04*g07*g011*gm5*gm8*s + CL*g03*g04*g08*g011*gm5*gm7*s +
MATLAB Solution Continued 8:
CL*g03*g05*g07*g011*gm4*gm8*s + CL*g03*g05*g08*g011*gm4*gm7*s + CL*g03*g07*g08*g011*gm4*gm5*s +
CL*g04*g05*g07*g011*gm3*gm8*s + CL*g04*g05*g08*g011*gm3*gm7*s + CL*g04*g07*g08*g011*gm3*gm5*s +
CL*g05*g07*g08*g011*gm3*gm4*s + CL*g01*g03*g06*gm2*gm4*gm5*s + CL*g01*g02*g03*gm4*gm5*gm8*s +
CL*g01*g03*g04*gm2*gm5*gm8*s + CL*g01*g03*g05*gm2*gm4*gm8*s + CL*g01*g03*g06*gm2*gm4*gm7*s +
CL*g01*g03*g08*gm2*gm4*gm5*s + CL*g01*g02*g06*gm3*gm5*gm7*s + CL*g02*g03*g06*gm1*gm5*gm7*s +
CL*g02*g05*g06*gm1*gm3*gm7*s + CL*g02*g06*g07*gm1*gm3*gm5*s + CL*g01*g02*g03*gm4*gm7*gm8*s +
CL*g01*g02*g06*gm4*gm5*gm7*s + CL*g01*g03*g04*gm2*gm7*gm8*s + CL*g01*g03*g07*gm2*gm4*gm8*s +
CL*g01*g03*g08*gm2*gm4*gm7*s + CL*g01*g04*g06*gm2*gm5*gm7*s + CL*g01*g05*g06*gm2*gm4*gm7*s +
CL*g01*g06*g07*gm2*gm4*gm5*s + CL*g01*g02*g03*gm5*gm7*gm8*s + CL*g01*g02*g05*gm3*gm7*gm8*s +
CL*g01*g02*g07*gm3*gm5*gm8*s + CL*g01*g02*g08*gm3*gm5*gm7*s + CL*g01*g03*g06*gm4*gm5*gm7*s +
CL*g01*g04*g06*gm3*gm5*gm7*s + CL*g01*g05*g06*gm3*gm4*gm7*s + CL*g01*g06*g07*gm3*gm4*gm5*s +
CL*g02*g03*g05*gm1*gm7*gm8*s + CL*g02*g03*g07*gm1*gm5*gm8*s + CL*g02*g03*g08*gm1*gm5*gm7*s +
CL*g02*g05*g07*gm1*gm3*gm8*s + CL*g02*g05*g08*gm1*gm3*gm7*s + CL*g02*g07*g08*gm1*gm3*gm5*s +
CL*g03*g04*g06*gm1*gm5*gm7*s + CL*g03*g05*g06*gm1*gm4*gm7*s + CL*g03*g06*g07*gm1*gm4*gm5*s +
CL*g04*g05*g06*gm1*gm3*gm7*s + CL*g04*g06*g07*gm1*gm3*gm5*s + CL*g05*g06*g07*gm1*gm3*gm4*s +
CL*g01*g02*g04*gm5*gm7*gm8*s + CL*g01*g02*g05*gm4*gm7*gm8*s + CL*g01*g02*g07*gm4*gm5*gm8*s +
CL*g01*g02*g08*gm4*gm5*gm7*s + CL*g01*g04*g05*gm2*gm7*gm8*s + CL*g01*g04*g07*gm2*gm5*gm8*s +
CL*g01*g04*g08*gm2*gm5*gm7*s + CL*g01*g05*g07*gm2*gm4*gm8*s + CL*g01*g05*g08*gm2*gm4*gm7*s +
CL*g01*g07*g08*gm2*gm4*gm5*s + CL*g02*g03*g06*gm4*gm5*gm7*s + CL*g02*g04*g06*gm3*gm5*gm7*s +
CL*g02*g05*g06*gm3*gm4*gm7*s + CL*g02*g06*g07*gm3*gm4*gm5*s + CL*g03*g04*g06*gm2*gm5*gm7*s +
CL*g03*g05*g06*gm2*gm4*gm7*s + CL*g03*g06*g07*gm2*gm4*gm5*s + CL*g04*g05*g06*gm2*gm3*gm7*s +
CL*g04*g06*g07*gm2*gm3*gm5*s + CL*g05*g06*g07*gm2*gm3*gm4*s + CL*g01*g03*g04*gm5*gm7*gm8*s +
CL*g01*g03*g05*gm4*gm7*gm8*s + CL*g01*g03*g07*gm4*gm5*gm8*s + CL*g01*g03*g08*gm4*gm5*gm7*s +
CL*g01*g04*g05*gm3*gm7*gm8*s + CL*g01*g04*g07*gm3*gm5*gm8*s + CL*g01*g04*g08*gm3*gm5*gm7*s +
CL*g01*g05*g07*gm3*gm4*gm8*s + CL*g01*g05*g08*gm3*gm4*gm7*s + CL*g01*g07*g08*gm3*gm4*gm5*s +
CL*g03*g04*g05*gm1*gm7*gm8*s + CL*g03*g04*g07*gm1*gm5*gm8*s + CL*g03*g04*g08*gm1*gm5*gm7*s +
CL*g03*g05*g07*gm1*gm4*gm8*s + CL*g03*g05*g08*gm1*gm4*gm7*s + CL*g03*g07*g08*gm1*gm4*gm5*s +
CL*g04*g05*g07*gm1*gm3*gm8*s + CL*g04*g05*g08*gm1*gm3*gm7*s + CL*g04*g07*g08*gm1*gm3*gm5*s +
CL*g05*g07*g08*gm1*gm3*gm4*s + CL*g02*g03*g04*gm5*gm7*gm8*s + CL*g02*g03*g05*gm4*gm7*gm8*s +
CL*g02*g03*g07*gm4*gm5*gm8*s + CL*g02*g03*g08*gm4*gm5*gm7*s + CL*g02*g04*g05*gm3*gm7*gm8*s +
CL*g02*g04*g07*gm3*gm5*gm8*s + CL*g02*g04*g08*gm3*gm5*gm7*s + CL*g02*g05*g07*gm3*gm4*gm8*s +
CL*g02*g05*g08*gm3*gm4*gm7*s + CL*g02*g07*g08*gm3*gm4*gm5*s + CL*g03*g04*g05*gm2*gm7*gm8*s +
CL*g03*g04*g07*gm2*gm5*gm8*s + CL*g03*g04*g08*gm2*gm5*gm7*s + CL*g03*g05*g07*gm2*gm4*gm8*s +
CL*g03*g05*g08*gm2*gm4*gm7*s + CL*g03*g07*g08*gm2*gm4*gm5*s + CL*g04*g05*g07*gm2*gm3*gm8*s +
CL*g04*g05*g08*gm2*gm3*gm7*s + CL*g04*g07*g08*gm2*gm3*gm5*s + CL*g05*g07*g08*gm2*gm3*gm4*s +
CL*g01*g03*g011*gm4*gm5*gm8*s + CL*g01*g02*g011*gm5*gm7*gm8*s + CL*g01*g03*g011*gm4*gm7*gm8*s +
CL*g01*g06*g011*gm4*gm5*gm7*s + CL*g02*g06*g011*gm3*gm5*gm7*s + CL*g01*g04*g011*gm5*gm7*gm8*s +
CL*g01*g05*g011*gm4*gm7*gm8*s + CL*g01*g07*g011*gm4*gm5*gm8*s + CL*g01*g08*g011*gm4*gm5*gm7*s +
CL*g02*g03*g011*gm5*gm7*gm8*s + CL*g02*g05*g011*gm3*gm7*gm8*s + CL*g02*g07*g011*gm3*gm5*gm8*s +
CL*g02*g08*g011*gm3*gm5*gm7*s + CL*g03*g06*g011*gm4*gm5*gm7*s + CL*g04*g06*g011*gm3*gm5*gm7*s +
CL*g05*g06*g011*gm3*gm4*gm7*s + CL*g06*g07*g011*gm3*gm4*gm5*s + CL*g03*g04*g011*gm5*gm7*gm8*s +
CL*g03*g05*g011*gm4*gm7*gm8*s + CL*g03*g07*g011*gm4*gm5*gm8*s + CL*g03*g08*g011*gm4*gm5*gm7*s +
CL*g04*g05*g011*gm3*gm7*gm8*s + CL*g04*g07*g011*gm3*gm5*gm8*s + CL*g04*g08*g011*gm3*gm5*gm7*s +
CL*g05*g07*g011*gm3*gm4*gm8*s + CL*g05*g08*g011*gm3*gm4*gm7*s + CL*g07*g08*g011*gm3*gm4*gm5*s +
CL*g01*g03*gm2*gm4*gm5*gm8*s + CL*g02*g06*gm1*gm3*gm5*gm7*s + CL*g01*g03*gm2*gm4*gm7*gm8*s +
CL*g01*g06*gm2*gm4*gm5*gm7*s + CL*g01*g02*gm3*gm5*gm7*gm8*s + CL*g01*g06*gm3*gm4*gm5*gm7*s +
CL*g02*g03*gm1*gm5*gm7*gm8*s + CL*g02*g05*gm1*gm3*gm7*gm8*s + CL*g02*g07*gm1*gm3*gm5*gm8*s +
CL*g02*g08*gm1*gm3*gm5*gm7*s + CL*g03*g06*gm1*gm4*gm5*gm7*s + CL*g04*g06*gm1*gm3*gm5*gm7*s +
CL*g05*g06*gm1*gm3*gm4*gm7*s + CL*g06*g07*gm1*gm3*gm4*gm5*s + CL*g01*g02*gm4*gm5*gm7*gm8*s +
CL*g01*g04*gm2*gm5*gm7*gm8*s + CL*g01*g05*gm2*gm4*gm7*gm8*s + CL*g01*g07*gm2*gm4*gm5*gm8*s +
CL*g01*g08*gm2*gm4*gm5*gm7*s + CL*g02*g06*gm3*gm4*gm5*gm7*s + CL*g03*g06*gm2*gm4*gm5*gm7*s +
CL*g04*g06*gm2*gm3*gm5*gm7*s + CL*g05*g06*gm2*gm3*gm4*gm7*s + CL*g06*g07*gm2*gm3*gm4*gm5*s +
CL*g01*g03*gm4*gm5*gm7*gm8*s + CL*g01*g04*gm3*gm5*gm7*gm8*s + CL*g01*g05*gm3*gm4*gm7*gm8*s +
CL*g01*g07*gm3*gm4*gm5*gm8*s + CL*g01*g08*gm3*gm4*gm5*gm7*s + CL*g03*g04*gm1*gm5*gm7*gm8*s +
CL*g03*g05*gm1*gm4*gm7*gm8*s + CL*g03*g07*gm1*gm4*gm5*gm8*s + CL*g03*g08*gm1*gm4*gm5*gm7*s +
CL*g04*g05*gm1*gm3*gm7*gm8*s + CL*g04*g07*gm1*gm3*gm5*gm8*s + CL*g04*g08*gm1*gm3*gm5*gm7*s +
CL*g05*g07*gm1*gm3*gm4*gm8*s + CL*g05*g08*gm1*gm3*gm4*gm7*s + CL*g07*g08*gm1*gm3*gm4*gm5*s +
CL*g02*g03*gm4*gm5*gm7*gm8*s + CL*g02*g04*gm3*gm5*gm7*gm8*s + CL*g02*g05*gm3*gm4*gm7*gm8*s +
CL*g02*g07*gm3*gm4*gm5*gm8*s + CL*g02*g08*gm3*gm4*gm5*gm7*s + CL*g03*g04*gm2*gm5*gm7*gm8*s +
CL*g03*g05*gm2*gm4*gm7*gm8*s + CL*g03*g07*gm2*gm4*gm5*gm8*s + CL*g03*g08*gm2*gm4*gm5*gm7*s +
CL*g04*g05*gm2*gm3*gm7*gm8*s + CL*g04*g07*gm2*gm3*gm5*gm8*s + CL*g04*g08*gm2*gm3*gm5*gm7*s +
CL*g05*g07*gm2*gm3*gm4*gm8*s + CL*g05*g08*gm2*gm3*gm4*gm7*s + CL*g07*g08*gm2*gm3*gm4*gm5*s +
CL*g01*g011*gm4*gm5*gm7*gm8*s + CL*g02*g011*gm3*gm5*gm7*gm8*s + CL*g06*g011*gm3*gm4*gm5*gm7*s +
CL*g03*g011*gm4*gm5*gm7*gm8*s + CL*g04*g011*gm3*gm5*gm7*gm8*s + CL*g05*g011*gm3*gm4*gm7*gm8*s +
CL*g07*g011*gm3*gm4*gm5*gm8*s + CL*g08*g011*gm3*gm4*gm5*gm7*s + CL*g02*gm1*gm3*gm5*gm7*gm8*s +
CL*g06*gm1*gm3*gm4*gm5*gm7*s + CL*g01*gm2*gm4*gm5*gm7*gm8*s + CL*g06*gm2*gm3*gm4*gm5*gm7*s +
CL*g01*gm3*gm4*gm5*gm7*gm8*s + CL*g03*gm1*gm4*gm5*gm7*gm8*s + CL*g04*gm1*gm3*gm5*gm7*gm8*s +
CL*g05*gm1*gm3*gm4*gm7*gm8*s + CL*g07*gm1*gm3*gm4*gm5*gm8*s + CL*g08*gm1*gm3*gm4*gm5*gm7*s +
CL*g02*gm3*gm4*gm5*gm7*gm8*s + CL*g03*gm2*gm4*gm5*gm7*gm8*s + CL*g04*gm2*gm3*gm5*gm7*gm8*s +
CL*g05*gm2*gm3*gm4*gm7*gm8*s + CL*g07*gm2*gm3*gm4*gm5*gm8*s + CL*g08*gm2*gm3*gm4*gm5*gm7*s +
CL*g011*gm3*gm4*gm5*gm7*gm8*s + CL*gm1*gm3*gm4*gm5*gm7*gm8*s + CL*gm2*gm3*gm4*gm5*gm7*gm8*s)
MATLAB Solution Continued 9:
We now (finally) have a complete analytic expression !
Vinp*g06*g07*g011*gm1*gm3*gm4*gm8 + Vinp*g03*g08*g011*gm1*gm4*gm7*gm8 +
Vinp*g04*g08*g011*gm1*gm3*gm7*gm8 + Vinp*g07*g08*g011*gm1*gm3*gm4*gm8 +
Vinp*g02*g06*gm1*gm3*gm4*gm5*gm7 + Vinp*g03*g06*gm1*gm2*gm4*gm5*gm7 +
Vinp*g04*g06*gm1*gm2*gm3*gm5*gm7 + Vinp*g05*g06*gm1*gm2*gm3*gm4*gm7 +
Vinp*g06*g07*gm1*gm2*gm3*gm4*gm5 + Vinp*g02*g06*gm1*gm3*gm4*gm5*gm8 +
Vinp*g03*g06*gm1*gm2*gm4*gm5*gm8 + Vinp*g04*g06*gm1*gm2*gm3*gm5*gm8 +
Vinp*g05*g06*gm1*gm2*gm3*gm4*gm8 + Vinp*g02*g03*gm1*gm4*gm5*gm7*gm8 +
Vinp*g02*g04*gm1*gm3*gm5*gm7*gm8 + Vinp*g02*g05*gm1*gm3*gm4*gm7*gm8 +
Vinp*g02*g07*gm1*gm3*gm4*gm5*gm8 + Vinp*g02*g08*gm1*gm3*gm4*gm5*gm7 +
Vinp*g03*g04*gm1*gm2*gm5*gm7*gm8 + Vinp*g03*g05*gm1*gm2*gm4*gm7*gm8 +
Vinp*g03*g07*gm1*gm2*gm4*gm5*gm8 + Vinp*g03*g08*gm1*gm2*gm4*gm5*gm7 +
Vinp*g04*g05*gm1*gm2*gm3*gm7*gm8 + Vinp*g04*g07*gm1*gm2*gm3*gm5*gm8 +
Vinp*g04*g08*gm1*gm2*gm3*gm5*gm7 + Vinp*g05*g07*gm1*gm2*gm3*gm4*gm8 +
Vinp*g05*g08*gm1*gm2*gm3*gm4*gm7 + Vinp*g07*g08*gm1*gm2*gm3*gm4*gm5 +
Vinp*g02*g06*gm1*gm3*gm4*gm7*gm8 + Vinp*g03*g06*gm1*gm2*gm4*gm7*gm8 +
Vinp*g04*g06*gm1*gm2*gm3*gm7*gm8 + Vinp*g06*g07*gm1*gm2*gm3*gm4*gm8 +
Vinp*g02*g08*gm1*gm3*gm4*gm7*gm8 + Vinp*g03*g08*gm1*gm2*gm4*gm7*gm8 +
Vinp*g04*g08*gm1*gm2*gm3*gm7*gm8 + Vinp*g07*g08*gm1*gm2*gm3*gm4*gm8 +
Vinp*g06*g011*gm1*gm3*gm4*gm5*gm8 + Vinp*g06*g011*gm1*gm3*gm4*gm7*gm8 +
Vinp*g08*g011*gm1*gm3*gm4*gm7*gm8 + Vinp*g06*gm1*gm2*gm3*gm4*gm5*gm7 +
Vinp*g06*gm1*gm2*gm3*gm4*gm5*gm8 + Vinp*g02*gm1*gm3*gm4*gm5*gm7*gm8 +
Vinp*g03*gm1*gm2*gm4*gm5*gm7*gm8 + Vinp*g04*gm1*gm2*gm3*gm5*gm7*gm8 +
Vinp*g05*gm1*gm2*gm3*gm4*gm7*gm8 + Vinp*g07*gm1*gm2*gm3*gm4*gm5*gm8 +
Vinp*g08*gm1*gm2*gm3*gm4*gm5*gm7 + Vinp*g06*gm1*gm2*gm3*gm4*gm7*gm8 +
Vinp*g08*gm1*gm2*gm3*gm4*gm7*gm8 + Vinp*gm1*gm2*gm3*gm4*gm5*gm7*gm8)
/
(g01*g02*g03*g04*g07*gm8^2 + g01*g02*g03*g04*gm7*gm8^2 + g01*g02*g04*g07*gm3*gm8^2 +
g02*g03*g04*g07*gm1*gm8^2 + g01*g02*g04*gm3*gm7*gm8^2 + g02*g03*g04*gm1*gm7*gm8^2 +
g02*g04*g07*gm1*gm3*gm8^2 + g02*g04*gm1*gm3*gm7*gm8^2 + g01*g02*g03*g04*g05*g06*g07 +
g01*g02*g03*g04*g05*g06*g08 + g01*g02*g03*g04*g05*g07*g08 + g01*g02*g03*g04*g06*g07*g08 +
g01*g02*g03*g04*g05*g06*g011 + g01*g02*g03*g05*g06*g07*g08 + g01*g02*g04*g05*g06*g07*g08 +
g01*g02*g03*g04*g05*g08*g011 + g01*g02*g03*g04*g06*g07*g011 + g01*g03*g04*g05*g06*g07*g08 +
g02*g03*g04*g05*g06*g07*g08 + g01*g02*g03*g04*g07*g08*g011 + g01*g02*g03*g05*g06*g08*g011 +
g01*g02*g04*g05*g06*g07*g011 + g01*g02*g03*g06*g07*g08*g011 + g01*g02*g04*g05*g07*g08*g011 +
g01*g03*g04*g05*g06*g08*g011 + g02*g03*g04*g05*g06*g07*g011 + g01*g02*g05*g06*g07*g08*g011 +
g01*g03*g04*g06*g07*g08*g011 + g02*g03*g04*g05*g07*g08*g011 + g01*g04*g05*g06*g07*g08*g011 +
g02*g03*g05*g06*g07*g08*g011 + g03*g04*g05*g06*g07*g08*g011 + g01*g02*g03*g04*g05*g06*gm7 +
g01*g02*g03*g04*g06*g07*gm5 + g01*g02*g04*g05*g06*g07*gm3 + g02*g03*g04*g05*g06*g07*gm1 +
g01*g02*g03*g04*g05*g06*gm8 + g01*g02*g03*g04*g06*g08*gm5 + g01*g02*g03*g05*g06*g08*gm4 +
g01*g03*g04*g05*g06*g08*gm2 + g01*g02*g03*g04*g05*g07*gm8 + g01*g02*g03*g04*g05*g08*gm7 +
g01*g02*g03*g04*g07*g08*gm5 + g01*g02*g04*g05*g07*g08*gm3 + g02*g03*g04*g05*g07*g08*gm1 +
g01*g02*g03*g04*g06*g07*gm8 + g01*g02*g03*g04*g06*g08*gm7 + g01*g02*g03*g06*g07*g08*gm4 +
g01*g03*g04*g06*g07*g08*gm2 + g01*g02*g03*g04*g06*g011*gm5 + g01*g02*g03*g05*g06*g08*gm7 +
g01*g02*g03*g06*g07*g08*gm5 + g01*g02*g05*g06*g07*g08*gm3 + g02*g03*g05*g06*g07*g08*gm1 +
g01*g02*g03*g04*g07*g08*gm8 + g01*g02*g04*g05*g06*g08*gm7 + g01*g02*g04*g06*g07*g08*gm5 +
g01*g02*g05*g06*g07*g08*gm4 + g01*g04*g05*g06*g07*g08*gm2 + g01*g02*g03*g04*g05*g011*gm8 +
g01*g02*g03*g04*g06*g011*gm7 + g01*g02*g03*g04*g08*g011*gm5 + g01*g03*g04*g05*g06*g08*gm7 +
g01*g03*g04*g06*g07*g08*gm5 + g01*g03*g05*g06*g07*g08*gm4 + g01*g04*g05*g06*g07*g08*gm3 +
g03*g04*g05*g06*g07*g08*gm1 + g02*g03*g04*g05*g06*g08*gm7 + g02*g03*g04*g06*g07*g08*gm5 +
g02*g03*g05*g06*g07*g08*gm4 + g02*g04*g05*g06*g07*g08*gm3 + g03*g04*g05*g06*g07*g08*gm2 +
g01*g02*g03*g04*g07*g011*gm8 + g01*g02*g03*g04*g08*g011*gm7 + g01*g02*g03*g06*g08*g011*gm5 +
g01*g02*g04*g05*g06*g011*gm7 + g01*g02*g04*g06*g07*g011*gm5 + g01*g02*g03*g06*g08*g011*gm7 +
g01*g02*g04*g05*g07*g011*gm8 + g01*g02*g04*g05*g08*g011*gm7 + g01*g02*g04*g07*g08*g011*gm5 +
g01*g03*g04*g06*g08*g011*gm5 + g01*g03*g05*g06*g08*g011*gm4 + g02*g03*g04*g05*g06*g011*gm7 +
g02*g03*g04*g06*g07*g011*gm5 + g02*g04*g05*g06*g07*g011*gm3 + g01*g02*g05*g06*g08*g011*gm7 +
g01*g02*g06*g07*g08*g011*gm5 + g01*g03*g04*g06*g08*g011*gm7 + g01*g03*g06*g07*g08*g011*gm4 +
g02*g03*g04*g05*g07*g011*gm8 + g02*g03*g04*g05*g08*g011*gm7 + g02*g03*g04*g07*g08*g011*gm5 +
g02*g04*g05*g07*g08*g011*gm3 + g01*g04*g05*g06*g08*g011*gm7 + g01*g04*g06*g07*g08*g011*gm5 +
g01*g05*g06*g07*g08*g011*gm4 + g02*g03*g05*g06*g08*g011*gm7 + g02*g03*g06*g07*g08*g011*gm5 +
g02*g05*g06*g07*g08*g011*gm3 + g03*g04*g05*g06*g08*g011*gm7 + g03*g04*g06*g07*g08*g011*gm5 +
g03*g05*g06*g07*g08*g011*gm4 + g04*g05*g06*g07*g08*g011*gm3 + g01*g02*g03*g04*g06*gm5*gm7 +
g01*g02*g04*g05*g06*gm3*gm7 + g01*g02*g04*g06*g07*gm3*gm5 + g02*g03*g04*g05*g06*gm1*gm7 +
g02*g03*g04*g06*g07*gm1*gm5 + g02*g04*g05*g06*g07*gm1*gm3 + g01*g02*g03*g04*g06*gm5*gm8 +
g01*g02*g03*g06*g08*gm4*gm5 + g01*g02*g04*g05*g06*gm3*gm8 + g01*g03*g04*g06*g08*gm2*gm5 +
g01*g03*g05*g06*g08*gm2*gm4 + g02*g03*g04*g05*g06*gm1*gm8 + g01*g02*g03*g04*g05*gm7*gm8 +
g01*g02*g03*g04*g07*gm5*gm8 + g01*g02*g03*g04*g08*gm5*gm7 + g01*g02*g04*g05*g07*gm3*gm8 +
g01*g02*g04*g05*g08*gm3*gm7 + g01*g02*g04*g07*g08*gm3*gm5 + g02*g03*g04*g05*g07*gm1*gm8 +
g02*g03*g04*g05*g08*gm1*gm7 + g02*g03*g04*g07*g08*gm1*gm5 + g02*g04*g05*g07*g08*gm1*gm3 +
g01*g02*g03*g04*g06*gm7*gm8 + g01*g02*g03*g06*g08*gm4*gm7 + g01*g02*g04*g06*g07*gm3*gm8 +
Zoom in to look at a few terms
CL*g03*g05*g07*g011*gm4*gm8*s + CL*g03*g05*g08*g011*gm4*gm7*s + CL*g03*g07*g08*g011*gm4*gm5*s +
CL*g04*g05*g07*g011*gm3*gm8*s + CL*g04*g05*g08*g011*gm3*gm7*s + CL*g04*g07*g08*g011*gm3*gm5*s +
CL*g05*g07*g08*g011*gm3*gm4*s + CL*g01*g03*g06*gm2*gm4*gm5*s + CL*g01*g02*g03*gm4*gm5*gm8*s +
CL*g01*g03*g04*gm2*gm5*gm8*s + CL*g01*g03*g05*gm2*gm4*gm8*s + CL*g01*g03*g06*gm2*gm4*gm7*s +
CL*g01*g03*g08*gm2*gm4*gm5*s + CL*g01*g02*g06*gm3*gm5*gm7*s + CL*g02*g03*g06*gm1*gm5*gm7*s +
CL*g02*g05*g06*gm1*gm3*gm7*s + CL*g02*g06*g07*gm1*gm3*gm5*s + CL*g01*g02*g03*gm4*gm7*gm8*s +
CL*g01*g02*g06*gm4*gm5*gm7*s + CL*g01*g03*g04*gm2*gm7*gm8*s + CL*g01*g03*g07*gm2*gm4*gm8*s +
CL*g01*g03*g08*gm2*gm4*gm7*s + CL*g01*g04*g06*gm2*gm5*gm7*s + CL*g01*g05*g06*gm2*gm4*gm7*s +
CL*g01*g06*g07*gm2*gm4*gm5*s + CL*g01*g02*g03*gm5*gm7*gm8*s + CL*g01*g02*g05*gm3*gm7*gm8*s +
CL*g01*g02*g07*gm3*gm5*gm8*s + CL*g01*g02*g08*gm3*gm5*gm7*s + CL*g01*g03*g06*gm4*gm5*gm7*s +
CL*g01*g04*g06*gm3*gm5*gm7*s + CL*g01*g05*g06*gm3*gm4*gm7*s + CL*g01*g06*g07*gm3*gm4*gm5*s +
CL*g02*g03*g05*gm1*gm7*gm8*s + CL*g02*g03*g07*gm1*gm5*gm8*s + CL*g02*g03*g08*gm1*gm5*gm7*s +
CL*g02*g05*g07*gm1*gm3*gm8*s + CL*g02*g05*g08*gm1*gm3*gm7*s + CL*g02*g07*g08*gm1*gm3*gm5*s +
CL*g03*g04*g06*gm1*gm5*gm7*s + CL*g03*g05*g06*gm1*gm4*gm7*s + CL*g03*g06*g07*gm1*gm4*gm5*s +
CL*g04*g05*g06*gm1*gm3*gm7*s + CL*g04*g06*g07*gm1*gm3*gm5*s + CL*g05*g06*g07*gm1*gm3*gm4*s +
CL*g01*g02*g04*gm5*gm7*gm8*s + CL*g01*g02*g05*gm4*gm7*gm8*s + CL*g01*g02*g07*gm4*gm5*gm8*s +
CL*g01*g02*g08*gm4*gm5*gm7*s + CL*g01*g04*g05*gm2*gm7*gm8*s + CL*g01*g04*g07*gm2*gm5*gm8*s +
CL*g01*g04*g08*gm2*gm5*gm7*s + CL*g01*g05*g07*gm2*gm4*gm8*s + CL*g01*g05*g08*gm2*gm4*gm7*s +
CL*g01*g07*g08*gm2*gm4*gm5*s + CL*g02*g03*g06*gm4*gm5*gm7*s + CL*g02*g04*g06*gm3*gm5*gm7*s +
CL*g02*g05*g06*gm3*gm4*gm7*s + CL*g02*g06*g07*gm3*gm4*gm5*s + CL*g03*g04*g06*gm2*gm5*gm7*s +
CL*g03*g05*g06*gm2*gm4*gm7*s + CL*g03*g06*g07*gm2*gm4*gm5*s + CL*g04*g05*g06*gm2*gm3*gm7*s +
CL*g04*g06*g07*gm2*gm3*gm5*s + CL*g05*g06*g07*gm2*gm3*gm4*s + CL*g01*g03*g04*gm5*gm7*gm8*s +
CL*g01*g03*g05*gm4*gm7*gm8*s + CL*g01*g03*g07*gm4*gm5*gm8*s + CL*g01*g03*g08*gm4*gm5*gm7*s +
CL*g01*g04*g05*gm3*gm7*gm8*s + CL*g01*g04*g07*gm3*gm5*gm8*s + CL*g01*g04*g08*gm3*gm5*gm7*s +
CL*g01*g05*g07*gm3*gm4*gm8*s + CL*g01*g05*g08*gm3*gm4*gm7*s + CL*g01*g07*g08*gm3*gm4*gm5*s +
CL*g03*g04*g05*gm1*gm7*gm8*s + CL*g03*g04*g07*gm1*gm5*gm8*s + CL*g03*g04*g08*gm1*gm5*gm7*s +
CL*g03*g05*g07*gm1*gm4*gm8*s + CL*g03*g05*g08*gm1*gm4*gm7*s + CL*g03*g07*g08*gm1*gm4*gm5*s +
CL*g04*g05*g07*gm1*gm3*gm8*s + CL*g04*g05*g08*gm1*gm3*gm7*s + CL*g04*g07*g08*gm1*gm3*gm5*s +
CL*g05*g07*g08*gm1*gm3*gm4*s + CL*g02*g03*g04*gm5*gm7*gm8*s + CL*g02*g03*g05*gm4*gm7*gm8*s +
CL*g02*g03*g07*gm4*gm5*gm8*s + CL*g02*g03*g08*gm4*gm5*gm7*s + CL*g02*g04*g05*gm3*gm7*gm8*s +
CL*g02*g04*g07*gm3*gm5*gm8*s + CL*g02*g04*g08*gm3*gm5*gm7*s + CL*g02*g05*g07*gm3*gm4*gm8*s +
CL*g02*g05*g08*gm3*gm4*gm7*s + CL*g02*g07*g08*gm3*gm4*gm5*s + CL*g03*g04*g05*gm2*gm7*gm8*s +
CL*g03*g04*g07*gm2*gm5*gm8*s + CL*g03*g04*g08*gm2*gm5*gm7*s + CL*g03*g05*g07*gm2*gm4*gm8*s +
CL*g03*g05*g08*gm2*gm4*gm7*s + CL*g03*g07*g08*gm2*gm4*gm5*s + CL*g04*g05*g07*gm2*gm3*gm8*s +
CL*g04*g05*g08*gm2*gm3*gm7*s + CL*g04*g07*g08*gm2*gm3*gm5*s + CL*g05*g07*g08*gm2*gm3*gm4*s +
CL*g01*g03*g011*gm4*gm5*gm8*s + CL*g01*g02*g011*gm5*gm7*gm8*s + CL*g01*g03*g011*gm4*gm7*gm8*s +
CL*g01*g06*g011*gm4*gm5*gm7*s + CL*g02*g06*g011*gm3*gm5*gm7*s + CL*g01*g04*g011*gm5*gm7*gm8*s +
CL*g01*g05*g011*gm4*gm7*gm8*s + CL*g01*g07*g011*gm4*gm5*gm8*s + CL*g01*g08*g011*gm4*gm5*gm7*s +
CL*g02*g03*g011*gm5*gm7*gm8*s + CL*g02*g05*g011*gm3*gm7*gm8*s + CL*g02*g07*g011*gm3*gm5*gm8*s +
CL*g02*g08*g011*gm3*gm5*gm7*s + CL*g03*g06*g011*gm4*gm5*gm7*s + CL*g04*g06*g011*gm3*gm5*gm7*s +
CL*g05*g06*g011*gm3*gm4*gm7*s + CL*g06*g07*g011*gm3*gm4*gm5*s + CL*g03*g04*g011*gm5*gm7*gm8*s +
CL*g03*g05*g011*gm4*gm7*gm8*s + CL*g03*g07*g011*gm4*gm5*gm8*s + CL*g03*g08*g011*gm4*gm5*gm7*s +
CL*g04*g05*g011*gm3*gm7*gm8*s + CL*g04*g07*g011*gm3*gm5*gm8*s + CL*g04*g08*g011*gm3*gm5*gm7*s +
CL*g05*g07*g011*gm3*gm4*gm8*s + CL*g05*g08*g011*gm3*gm4*gm7*s + CL*g07*g08*g011*gm3*gm4*gm5*s +
CL*g01*g03*gm2*gm4*gm5*gm8*s + CL*g02*g06*gm1*gm3*gm5*gm7*s + CL*g01*g03*gm2*gm4*gm7*gm8*s +
CL*g01*g06*gm2*gm4*gm5*gm7*s + CL*g01*g02*gm3*gm5*gm7*gm8*s + CL*g01*g06*gm3*gm4*gm5*gm7*s +
CL*g02*g03*gm1*gm5*gm7*gm8*s + CL*g02*g05*gm1*gm3*gm7*gm8*s + CL*g02*g07*gm1*gm3*gm5*gm8*s +
CL*g02*g08*gm1*gm3*gm5*gm7*s + CL*g03*g06*gm1*gm4*gm5*gm7*s + CL*g04*g06*gm1*gm3*gm5*gm7*s +
CL*g05*g06*gm1*gm3*gm4*gm7*s + CL*g06*g07*gm1*gm3*gm4*gm5*s + CL*g01*g02*gm4*gm5*gm7*gm8*s +
CL*g01*g04*gm2*gm5*gm7*gm8*s + CL*g01*g05*gm2*gm4*gm7*gm8*s + CL*g01*g07*gm2*gm4*gm5*gm8*s +
CL*g01*g08*gm2*gm4*gm5*gm7*s + CL*g02*g06*gm3*gm4*gm5*gm7*s + CL*g03*g06*gm2*gm4*gm5*gm7*s +
CL*g04*g06*gm2*gm3*gm5*gm7*s + CL*g05*g06*gm2*gm3*gm4*gm7*s + CL*g06*g07*gm2*gm3*gm4*gm5*s +
CL*g01*g03*gm4*gm5*gm7*gm8*s + CL*g01*g04*gm3*gm5*gm7*gm8*s + CL*g01*g05*gm3*gm4*gm7*gm8*s +
CL*g01*g07*gm3*gm4*gm5*gm8*s + CL*g01*g08*gm3*gm4*gm5*gm7*s + CL*g03*g04*gm1*gm5*gm7*gm8*s +
CL*g03*g05*gm1*gm4*gm7*gm8*s + CL*g03*g07*gm1*gm4*gm5*gm8*s + CL*g03*g08*gm1*gm4*gm5*gm7*s +
CL*g04*g05*gm1*gm3*gm7*gm8*s + CL*g04*g07*gm1*gm3*gm5*gm8*s + CL*g04*g08*gm1*gm3*gm5*gm7*s +
CL*g05*g07*gm1*gm3*gm4*gm8*s + CL*g05*g08*gm1*gm3*gm4*gm7*s + CL*g07*g08*gm1*gm3*gm4*gm5*s +
CL*g02*g03*gm4*gm5*gm7*gm8*s + CL*g02*g04*gm3*gm5*gm7*gm8*s + CL*g02*g05*gm3*gm4*gm7*gm8*s +
CL*g02*g07*gm3*gm4*gm5*gm8*s + CL*g02*g08*gm3*gm4*gm5*gm7*s + CL*g03*g04*gm2*gm5*gm7*gm8*s +
CL*g03*g05*gm2*gm4*gm7*gm8*s + CL*g03*g07*gm2*gm4*gm5*gm8*s + CL*g03*g08*gm2*gm4*gm5*gm7*s +
CL*g04*g05*gm2*gm3*gm7*gm8*s + CL*g04*g07*gm2*gm3*gm5*gm8*s + CL*g04*g08*gm2*gm3*gm5*gm7*s +
CL*g05*g07*gm2*gm3*gm4*gm8*s + CL*g05*g08*gm2*gm3*gm4*gm7*s + CL*g07*g08*gm2*gm3*gm4*gm5*s +
CL*g01*g011*gm4*gm5*gm7*gm8*s + CL*g02*g011*gm3*gm5*gm7*gm8*s + CL*g06*g011*gm3*gm4*gm5*gm7*s +
CL*g03*g011*gm4*gm5*gm7*gm8*s + CL*g04*g011*gm3*gm5*gm7*gm8*s + CL*g05*g011*gm3*gm4*gm7*gm8*s +
CL*g07*g011*gm3*gm4*gm5*gm8*s + CL*g08*g011*gm3*gm4*gm5*gm7*s + CL*g02*gm1*gm3*gm5*gm7*gm8*s +
CL*g06*gm1*gm3*gm4*gm5*gm7*s + CL*g01*gm2*gm4*gm5*gm7*gm8*s + CL*g06*gm2*gm3*gm4*gm5*gm7*s +
CL*g01*gm3*gm4*gm5*gm7*gm8*s + CL*g03*gm1*gm4*gm5*gm7*gm8*s + CL*g04*gm1*gm3*gm5*gm7*gm8*s +
CL*g05*gm1*gm3*gm4*gm7*gm8*s + CL*g07*gm1*gm3*gm4*gm5*gm8*s + CL*g08*gm1*gm3*gm4*gm5*gm7*s +
CL*g02*gm3*gm4*gm5*gm7*gm8*s + CL*g03*gm2*gm4*gm5*gm7*gm8*s + CL*g04*gm2*gm3*gm5*gm7*gm8*s +
CL*g05*gm2*gm3*gm4*gm7*gm8*s + CL*g07*gm2*gm3*gm4*gm5*gm8*s + CL*g08*gm2*gm3*gm4*gm5*gm7*s +
CL*g011*gm3*gm4*gm5*gm7*gm8*s + CL*gm1*gm3*gm4*gm5*gm7*gm8*s + CL*gm2*gm3*gm4*gm5*gm7*gm8*s)
Vinp*g08*gm1*gm2*gm3*gm4*gm5*gm7+ Vinp*g06*gm1*gm2*gm3*gm4*gm7*gm8 +
Vinp*g08*gm1*gm2*gm3*gm4*gm7*gm8 + Vinp*gm1*gm2*gm3*gm4*gm5*gm7*gm8)
/
(g01*g02*g03*g04*g07*gm8^2 + g01*g02*g03*g04*gm7*gm8^2 +
g01*g02*g04*g07*gm3*gm8^2 + g02*g03*g04*g07*gm1*gm8^2 +
g01*g02*g04*gm3*gm7*gm8^2 + g02*g03*g04*gm1*gm7*gm8^2 +
Individual product terms have product of 7 small-signal parameters
CL*g02*gm3*gm4*gm5*gm7*gm8*s + CL*g03*gm2*gm4*gm5*gm7*gm8*s +
CL*g04*gm2*gm3*gm5*gm7*gm8*s + CL*g05*gm2*gm3*gm4*gm7*gm8*s +
CL*g07*gm2*gm3*gm4*gm5*gm8*s + CL*g08*gm2*gm3*gm4*gm5*gm7*s +
CL*g011*gm3*gm4*gm5*gm7*gm8*s + CL*gm1*gm3*gm4*gm5*gm7*gm8*s +
CL*gm2*gm3*gm4*gm5*gm7*gm8*s)
• Approximately 2000 factors in output characteristics• Approximately 14,000 small-signal parameter appearances• GB expression much longer
MATLAB simulation results using Symbolic Math Toolbox
MATLAB Solution:
Differential Analysis with Vd = Vin+ - Vin-
GainAv = (g01*g03*g04*g07*gm2*gm8^2 + g02*g03*g04*g07*gm1*gm8^2 + g02*g03*g07*g011*gm1*gm8^2 +
g03*g04*g07*g011*gm1*gm8^2 + g01*g03*g04*gm2*gm7*gm8^2 + g01*g03*g07*gm2*gm4*gm8^2 +
g01*g04*g07*gm2*gm3*gm8^2 + g02*g03*g04*gm1*gm7*gm8^2 + g02*g03*g07*gm1*gm4*gm8^2 +
g02*g04*g07*gm1*gm3*gm8^2 + 2*g03*g04*g07*gm1*gm2*gm8^2 + g02*g03*g011*gm1*gm7*gm8^2 +
g02*g07*g011*gm1*gm3*gm8^2 + g03*g04*g011*gm1*gm7*gm8^2 + g03*g07*g011*gm1*gm4*gm8^2 +
g04*g07*g011*gm1*gm3*gm8^2 + g01*g03*gm2*gm4*gm7*gm8^2 + g01*g04*gm2*gm3*gm7*gm8^2 +
g01*g07*gm2*gm3*gm4*gm8^2 + g02*g03*gm1*gm4*gm7*gm8^2 + g02*g04*gm1*gm3*gm7*gm8^2 +
g02*g07*gm1*gm3*gm4*gm8^2 + 2*g03*g04*gm1*gm2*gm7*gm8^2 + 2*g03*g07*gm1*gm2*gm4*gm8^2 +
2*g04*g07*gm1*gm2*gm3*gm8^2 + g02*g011*gm1*gm3*gm7*gm8^2 + g03*g011*gm1*gm4*gm7*gm8^2 +
g04*g011*gm1*gm3*gm7*gm8^2 + g07*g011*gm1*gm3*gm4*gm8^2 + g01*gm2*gm3*gm4*gm7*gm8^2 +
g02*gm1*gm3*gm4*gm7*gm8^2 + 2*g03*gm1*gm2*gm4*gm7*gm8^2 + 2*g04*gm1*gm2*gm3*gm7*gm8^2 +
2*g07*gm1*gm2*gm3*gm4*gm8^2 + g011*gm1*gm3*gm4*gm7*m8^2 + 2*gm1*gm2*gm3*gm4*gm7*gm8^2 +
g01*g03*g04*g05*g06*g07*gm2 + g02*g03*g04*g05*g06*g07*gm1 + g01*g03*g04*g05*g07*g08*gm2 +
g02*g03*g04*g05*g07*g08*gm1 + g01*g03*g04*g05*g06*g011*gm2 + g01*g03*g04*g05*g08*g011*gm2 +
g01*g03*g04*g06*g07*g011*gm2 + g01*g03*g04*g07*g08*g011*gm2 + g01*g04*g05*g06*g07*g011*gm2 +
g01*g04*g05*g07*g08*g011*gm2 + g03*g04*g05*g06*g07*g011*gm2 + g03*g04*g05*g07*g08*g011*gm2 +
g01*g03*g04*g05*g06*gm2*gm7 + g01*g03*g04*g06*g07*gm2*gm5 + g01*g03*g05*g06*g07*gm2*gm4 +
g01*g04*g05*g06*g07*gm2*gm3 + g02*g03*g04*g05*g06*gm1*gm7 + g02*g03*g04*g06*g07*gm1*gm5 +
g02*g03*g05*g06*g07*gm1*gm4 + g02*g04*g05*g06*g07*gm1*gm3 + 2*g03*g04*g05*g06*g07*gm1*gm2 +
g01*g03*g04*g05*g06*gm2*gm8 + g02*g03*g04*g05*g06*gm1*gm8 + g01*g03*g04*g05*g07*gm2*gm8 +
g01*g03*g04*g05*g08*gm2*gm7 + g01*g03*g04*g07*g08*gm2*gm5 + g01*g03*g05*g07*g08*gm2*gm4 +
g01*g04*g05*g07*g08*gm2*gm3 + g02*g03*g04*g05*g07*gm1*gm8 + g02*g03*g04*g05*g08*gm1*gm7 +
g02*g03*g04*g07*g08*gm1*gm5 + g02*g03*g05*g07*g08*gm1*gm4 + g02*g04*g05*g07*g08*gm1*gm3 +
2*g03*g04*g05*g07*g08*gm1*gm2 + g01*g03*g04*g06*g07*gm2*gm8 + g02*g03*g04*g06*g07*gm1*gm8 +
g01*g03*g04*g06*g011*gm2*gm5 + g01*g03*g05*g06*g011*gm2*gm4 + g01*g03*g04*g07*g08*gm2*gm8 +
g02*g03*g04*g07*g08*gm1*gm8 + g01*g03*g04*g05*g011*gm2*gm8 + g01*g03*g04*g06*g011*gm2*gm7 +
g01*g03*g04*g08*g011*gm2*gm5 + g01*g03*g05*g08*g011*gm2*gm4 + g01*g03*g06*g07*g011*gm2*gm4 +
g01*g03*g04*g07*g011*gm2*gm8 + g01*g03*g04*g08*g011*gm2*gm7 + g01*g03*g07*g08*g011*gm2*gm4 +
g01*g04*g05*g06*g011*gm2*gm7 + g01*g04*g06*g07*g011*gm2*gm5 + g01*g05*g06*g07*g011*gm2*gm4 +
g02*g03*g05*g06*g011*gm1*gm8 + g01*g04*g05*g07*g011*gm2*gm8 + g01*g04*g05*g08*g011*gm2*gm7 +
g01*g04*g07*g08*g011*gm2*gm5 + g01*g05*g07*g08*g011*gm2*gm4 + g02*g03*g06*g07*g011*gm1*gm8 +
g03*g04*g05*g06*g011*gm1*gm8 + g03*g04*g05*g06*g011*gm2*gm7 + g03*g04*g06*g07*g011*gm2*gm5 +
g03*g05*g06*g07*g011*gm2*gm4 + g04*g05*g06*g07*g011*gm2*gm3 + g02*g03*g07*g08*g011*gm1*gm8 +
g03*g04*g05*g07*g011*gm2*gm8 + g03*g04*g05*g08*g011*gm2*gm7 + g03*g04*g06*g07*g011*gm1*gm8 +
g03*g04*g07*g08*g011*gm2*gm5 + g03*g05*g07*g08*g011*gm2*gm4 + g04*g05*g07*g08*g011*gm2*gm3 +
g03*g04*g07*g08*g011*gm1*gm8 + g01*g03*g04*g06*gm2*gm5*gm7 + g01*g03*g05*g06*gm2*gm4*gm7 +
g01*g03*g06*g07*gm2*gm4*gm5 + g01*g04*g05*g06*gm2*gm3*gm7 + g01*g04*g06*g07*gm2*gm3*gm5 +
g01*g05*g06*g07*gm2*gm3*gm4 + g02*g03*g04*g06*gm1*gm5*gm7 + g02*g03*g05*g06*gm1*gm4*gm7 +
g02*g03*g06*g07*gm1*gm4*gm5 + g02*g04*g05*g06*gm1*gm3*gm7 + g02*g04*g06*g07*gm1*gm3*gm5 +
g02*g05*g06*g07*gm1*gm3*gm4 + 2*g03*g04*g05*g06*gm1*gm2*gm7 + 2*g03*g04*g06*g07*gm1*gm2*gm5 +
2*g03*g05*g06*g07*gm1*gm2*gm4 + 2*g04*g05*g06*g07*gm1*gm2*gm3 + g01*g03*g04*g06*gm2*gm5*gm8 +
g01*g03*g05*g06*gm2*gm4*gm8 + g01*g04*g05*g06*gm2*gm3*gm8 + g02*g03*g04*g06*gm1*gm5*gm8 +
g02*g03*g05*g06*gm1*gm4*gm8 + g02*g04*g05*g06*gm1*gm3*gm8 + 2*g03*g04*g05*g06*gm1*gm2*gm8 +
g01*g03*g04*g05*gm2*gm7*gm8 + g01*g03*g04*g07*gm2*gm5*gm8 + g01*g03*g04*g08*gm2*gm5*gm7 +
g01*g03*g05*g07*gm2*gm4*gm8 + g01*g03*g05*g08*gm2*gm4*gm7 + g01*g03*g07*g08*gm2*gm4*gm5 +
g01*g04*g05*g07*gm2*gm3*gm8 + g01*g04*g05*g08*gm2*gm3*gm7 + g01*g04*g07*g08*gm2*gm3*gm5 +
g01*g05*g07*g08*gm2*gm3*gm4 + g02*g03*g04*g05*gm1*gm7*gm8 + g02*g03*g04*g07*gm1*gm5*gm8 +
g02*g03*g04*g08*gm1*gm5*gm7 + g02*g03*g05*g07*gm1*gm4*gm8 + g02*g03*g05*g08*gm1*gm4*gm7 +
g02*g03*g07*g08*gm1*gm4*gm5 + g02*g04*g05*g07*gm1*gm3*gm8 + g02*g04*g05*g08*gm1*gm3*gm7 +
g02*g04*g07*g08*gm1*gm3*gm5 + g02*g05*g07*g08*gm1*gm3*gm4 + 2*g03*g04*g05*g07*gm1*gm2*gm8 +
2*g03*g04*g05*g08*gm1*gm2*gm7 + 2*g03*g04*g07*g08*gm1*gm2*gm5 + 2*g03*g05*g07*g08*gm1*gm2*gm4 +
2*g04*g05*g07*g08*gm1*gm2*gm3 + g01*g03*g04*g06*gm2*gm7*gm8 + g01*g03*g06*g07*gm2*gm4*gm8 +
g01*g04*g06*g07*gm2*gm3*gm8 + g02*g03*g04*g06*gm1*gm7*gm8 + g02*g03*g06*g07*gm1*gm4*gm8 +
g02*g04*g06*g07*gm1*gm3*gm8 + 2*g03*g04*g06*g07*gm1*gm2*gm8 + g01*g03*g06*g011*gm2*gm4*gm5 +
g01*g03*g04*g08*gm2*gm7*gm8 + g01*g03*g07*g08*gm2*gm4*gm8 + g01*g04*g07*g08*gm2*gm3*gm8 +
g02*g03*g04*g08*gm1*gm7*gm8 + g02*g03*g07*g08*gm1*gm4*gm8 + g02*g04*g07*g08*gm1*gm3*gm8 +
2*g03*g04*g07*g08*gm1*gm2*gm8 + g01*g03*g04*g011*gm2*gm5*gm8 + g01*g03*g05*g011*gm2*gm4*gm8 +
g01*g03*g06*g011*gm2*gm4*gm7 + g01*g03*g08*g011*gm2*gm4*gm5 + g01*g03*g04*g011*gm2*gm7*gm8 +
g01*g03*g07*g011*gm2*gm4*gm8 + g01*g03*g08*g011*gm2*gm4*gm7 + g01*g04*g06*g011*gm2*gm5*gm7 +
g01*g05*g06*g011*gm2*gm4*gm7 + g01*g06*g07*g011*gm2*gm4*gm5 + g02*g03*g06*g011*gm1*gm5*gm8 +
g02*g05*g06*g011*gm1*gm3*gm8 + g01*g04*g05*g011*gm2*gm7*gm8 + g01*g04*g07*g011*gm2*gm5*gm8 +
g01*g04*g08*g011*gm2*gm5*gm7 + g01*g05*g07*g011*gm2*gm4*gm8 + g01*g05*g08*g011*gm2*gm4*gm7 +
g01*g07*g08*g011*gm2*gm4*gm5 + g02*g03*g06*g011*gm1*gm7*gm8 + g02*g06*g07*g011*gm1*gm3*gm8 +
g03*g04*g06*g011*gm1*gm5*gm8 + g03*g04*g06*g011*gm2*gm5*gm7 + g03*g05*g06*g011*gm1*gm4*gm8 +
g03*g05*g06*g011*gm2*gm4*gm7 + g03*g06*g07*g011*gm2*gm4*gm5 + g04*g05*g06*g011*gm1*gm3*gm8 +
g04*g05*g06*g011*gm2*gm3*gm7 + g04*g06*g07*g011*gm2*gm3*gm5 + g05*g06*g07*g011*gm2*gm3*gm4 +
g02*g03*g08*g011*gm1*gm7*gm8 + g02*g07*g08*g011*gm1*gm3*gm8 + g03*g04*g05*g011*gm2*gm7*gm8 +
MATLAB Solution Continued 1:g03*g04*g06*g011*gm1*gm7*gm8 + g03*g04*g07*g011*gm2*gm5*gm8 + g03*g04*g08*g011*gm2*gm5*gm7 +
g03*g05*g07*g011*gm2*gm4*gm8 + g03*g05*g08*g011*gm2*gm4*gm7 + g03*g06*g07*g011*gm1*gm4*gm8 +
g03*g07*g08*g011*gm2*gm4*gm5 + g04*g05*g07*g011*gm2*gm3*gm8 + g04*g05*g08*g011*gm2*gm3*gm7 +
g04*g06*g07*g011*gm1*gm3*gm8 + g04*g07*g08*g011*gm2*gm3*gm5 + g05*g07*g08*g011*gm2*gm3*gm4 +
g03*g04*g08*g011*gm1*gm7*gm8 + g03*g07*g08*g011*gm1*gm4*gm8 + g04*g07*g08*g011*gm1*gm3*gm8 +
g01*g03*g06*gm2*gm4*gm5*gm7 + g01*g04*g06*gm2*gm3*gm5*gm7 + g01*g05*g06*gm2*gm3*gm4*gm7 +
g01*g06*g07*gm2*gm3*gm4*gm5 + g02*g03*g06*gm1*gm4*gm5*gm7 + g02*g04*g06*gm1*gm3*gm5*gm7 +
g02*g05*g06*gm1*gm3*gm4*gm7 + g02*g06*g07*gm1*gm3*gm4*gm5 + 2*g03*g04*g06*gm1*gm2*gm5*gm7 +
2*g03*g05*g06*gm1*gm2*gm4*gm7 + 2*g03*g06*g07*gm1*gm2*gm4*gm5 + 2*g04*g05*g06*gm1*gm2*gm3*gm7 +
2*g04*g06*g07*gm1*gm2*gm3*gm5 + 2*g05*g06*g07*gm1*gm2*gm3*gm4 + g01*g03*g06*gm2*gm4*gm5*gm8 +
g01*g04*g06*gm2*gm3*gm5*gm8 + g01*g05*g06*gm2*gm3*gm4*gm8 + g02*g03*g06*gm1*gm4*gm5*gm8 +
g02*g04*g06*gm1*gm3*gm5*gm8 + g02*g05*g06*gm1*gm3*gm4*gm8 + 2*g03*g04*g06*gm1*gm2*gm5*gm8 +
2*g03*g05*g06*gm1*gm2*gm4*gm8 + 2*g04*g05*g06*gm1*gm2*gm3*gm8 + g01*g03*g04*gm2*gm5*gm7*gm8 +
g01*g03*g05*gm2*gm4*gm7*gm8 + g01*g03*g07*gm2*gm4*gm5*gm8 + g01*g03*g08*gm2*gm4*gm5*gm7 +
g01*g04*g05*gm2*gm3*gm7*gm8 + g01*g04*g07*gm2*gm3*gm5*gm8 + g01*g04*g08*gm2*gm3*gm5*gm7 +
g01*g05*g07*gm2*gm3*gm4*gm8 + g01*g05*g08*gm2*gm3*gm4*gm7 + g01*g07*g08*gm2*gm3*gm4*gm5 +
g02*g03*g04*gm1*gm5*gm7*gm8 + g02*g03*g05*gm1*gm4*gm7*gm8 + g02*g03*g07*gm1*gm4*gm5*gm8 +
g02*g03*g08*gm1*gm4*gm5*gm7 + g02*g04*g05*gm1*gm3*gm7*gm8 + g02*g04*g07*gm1*gm3*gm5*gm8 +
g02*g04*g08*gm1*gm3*gm5*gm7 + g02*g05*g07*gm1*gm3*gm4*gm8 + g02*g05*g08*gm1*gm3*gm4*gm7 +
g02*g07*g08*gm1*gm3*gm4*gm5 + 2*g03*g04*g05*gm1*gm2*gm7*gm8 + 2*g03*g04*g07*gm1*gm2*gm5*gm8 +
2*g03*g04*g08*gm1*gm2*gm5*gm7 + 2*g03*g05*g07*gm1*gm2*gm4*gm8 + 2*g03*g05*g08*gm1*gm2*gm4*gm7 +
2*g03*g07*g08*gm1*gm2*gm4*gm5 + 2*g04*g05*g07*gm1*gm2*gm3*gm8 + 2*g04*g05*g08*gm1*gm2*gm3*gm7 +
2*g04*g07*g08*gm1*gm2*gm3*gm5 + 2*g05*g07*g08*gm1*gm2*gm3*gm4 + g01*g03*g06*gm2*gm4*gm7*gm8 +
g01*g04*g06*gm2*gm3*gm7*gm8 + g01*g06*g07*gm2*gm3*gm4*gm8 + g02*g03*g06*gm1*gm4*gm7*gm8 +
g02*g04*g06*gm1*gm3*gm7*gm8 + g02*g06*g07*gm1*gm3*gm4*gm8 + 2*g03*g04*g06*gm1*gm2*gm7*gm8 +
2*g03*g06*g07*gm1*gm2*gm4*gm8 + 2*g04*g06*g07*gm1*gm2*gm3*gm8 + g01*g03*g08*gm2*gm4*gm7*gm8 +
g01*g04*g08*gm2*gm3*gm7*gm8 + g01*g07*g08*gm2*gm3*gm4*gm8 + g02*g03*g08*gm1*gm4*gm7*gm8 +
g02*g04*g08*gm1*gm3*gm7*gm8 + g02*g07*g08*gm1*gm3*gm4*gm8 + 2*g03*g04*g08*gm1*gm2*gm7*gm8 +
2*g03*g07*g08*gm1*gm2*gm4*gm8 + 2*g04*g07*g08*gm1*gm2*gm3*gm8 + g01*g03*g011*gm2*gm4*gm5*gm8 +
g01*g03*g011*gm2*gm4*gm7*gm8 + g01*g06*g011*gm2*gm4*gm5*gm7 + g02*g06*g011*gm1*gm3*gm5*gm8 +
g01*g04*g011*gm2*gm5*gm7*gm8 + g01*g05*g011*gm2*gm4*gm7*gm8 + g01*g07*g011*gm2*gm4*gm5*gm8 +
g01*g08*g011*gm2*gm4*gm5*gm7 + g02*g06*g011*gm1*gm3*gm7*gm8 + g03*g06*g011*gm1*gm4*gm5*gm8 +
g03*g06*g011*gm2*gm4*gm5*gm7 + g04*g06*g011*gm1*gm3*gm5*gm8 + g04*g06*g011*gm2*gm3*gm5*gm7 +
g05*g06*g011*gm1*gm3*gm4*gm8 + g05*g06*g011*gm2*gm3*gm4*gm7 + g06*g07*g011*gm2*gm3*gm4*gm5 +
g02*g08*g011*gm1*gm3*gm7*gm8 + g03*g04*g011*gm2*gm5*gm7*gm8 + g03*g05*g011*gm2*gm4*gm7*gm8 +
g03*g06*g011*gm1*gm4*gm7*gm8 + g03*g07*g011*gm2*gm4*gm5*gm8 + g03*g08*g011*gm2*gm4*gm5*gm7 +
g04*g05*g011*gm2*gm3*gm7*gm8 + g04*g06*g011*gm1*gm3*gm7*gm8 + g04*g07*g011*gm2*gm3*gm5*gm8 +
g04*g08*g011*gm2*gm3*gm5*gm7 + g05*g07*g011*gm2*gm3*gm4*gm8 + g05*g08*g011*gm2*gm3*gm4*gm7 +
g06*g07*g011*gm1*gm3*gm4*gm8 + g07*g08*g011*gm2*gm3*gm4*gm5 + g03*g08*g011*gm1*gm4*gm7*gm8 +
g04*g08*g011*gm1*gm3*gm7*gm8 + g07*g08*g011*gm1*gm3*gm4*gm8 + g01*g06*gm2*gm3*gm4*gm5*gm7 +
g02*g06*gm1*gm3*gm4*gm5*gm7 + 2*g03*g06*gm1*gm2*gm4*gm5*gm7 + 2*g04*g06*gm1*gm2*gm3*gm5*gm7 +
2*g05*g06*gm1*gm2*gm3*gm4*gm7 + 2*g06*g07*gm1*gm2*gm3*gm4*gm5 + g01*g06*gm2*gm3*gm4*gm5*gm8 +
g02*g06*gm1*gm3*gm4*gm5*gm8 + 2*g03*g06*gm1*gm2*gm4*gm5*gm8 + 2*g04*g06*gm1*gm2*gm3*gm5*gm8 +
2*g05*g06*gm1*gm2*gm3*gm4*gm8 + g01*g03*gm2*gm4*gm5*gm7*gm8 + g01*g04*gm2*gm3*gm5*gm7*gm8 +
g01*g05*gm2*gm3*gm4*gm7*gm8 + g01*g07*gm2*gm3*gm4*gm5*gm8 + g01*g08*gm2*gm3*gm4*gm5*gm7 +
g02*g03*gm1*gm4*gm5*gm7*gm8 + g02*g04*gm1*gm3*gm5*gm7*gm8 + g02*g05*gm1*gm3*gm4*gm7*gm8 +
g02*g07*gm1*gm3*gm4*gm5*gm8 + g02*g08*gm1*gm3*gm4*gm5*gm7 + 2*g03*g04*gm1*gm2*gm5*gm7*gm8 +
2*g03*g05*gm1*gm2*gm4*gm7*gm8 + 2*g03*g07*gm1*gm2*gm4*gm5*gm8 + 2*g03*g08*gm1*gm2*gm4*gm5*gm7 +
2*g04*g05*gm1*gm2*gm3*gm7*gm8 + 2*g04*g07*gm1*gm2*gm3*gm5*gm8 + 2*g04*g08*gm1*gm2*gm3*gm5*gm7 +
2*g05*g07*gm1*gm2*gm3*gm4*gm8 + 2*g05*g08*gm1*gm2*gm3*gm4*gm7 + 2*g07*g08*gm1*gm2*gm3*gm4*gm5 +
g01*g06*gm2*gm3*gm4*gm7*gm8 + g02*g06*gm1*gm3*gm4*gm7*gm8 + 2*g03*g06*gm1*gm2*gm4*gm7*gm8 +
2*g04*g06*gm1*gm2*gm3*gm7*gm8 + 2*g06*g07*gm1*gm2*gm3*gm4*gm8 + g01*g08*gm2*gm3*gm4*gm7*gm8 +
g02*g08*gm1*gm3*gm4*gm7*gm8 + 2*g03*g08*gm1*gm2*gm4*gm7*gm8 + 2*g04*g08*gm1*gm2*gm3*gm7*gm8 +
2*g07*g08*gm1*gm2*gm3*gm4*gm8 + g01*g011*gm2*gm4*gm5*gm7*gm8 + g06*g011*gm1*gm3*gm4*gm5*gm8 +
g06*g011*gm2*gm3*gm4*gm5*gm7 + g03*g011*gm2*gm4*gm5*gm7*gm8 + g04*g011*gm2*gm3*gm5*gm7*gm8 +
g05*g011*gm2*gm3*gm4*gm7*gm8 + g06*g011*gm1*gm3*gm4*gm7*gm8 + g07*g011*gm2*gm3*gm4*gm5*gm8 +
g08*g011*gm2*gm3*gm4*gm5*gm7 + g08*g011*gm1*gm3*gm4*gm7*gm8 + 2*g06*gm1*gm2*gm3*gm4*gm5*gm7 +
2*g06*gm1*gm2*gm3*gm4*gm5*gm8 + g01*gm2*gm3*gm4*gm5*gm7*gm8 + g02*gm1*gm3*gm4*gm5*gm7*gm8 +
2*g03*gm1*gm2*gm4*gm5*gm7*gm8 + 2*g04*gm1*gm2*gm3*gm5*gm7*gm8 + 2*g05*gm1*gm2*gm3*gm4*gm7*gm8 +
2*g07*gm1*gm2*gm3*gm4*gm5*gm8 + 2*g08*gm1*gm2*gm3*gm4*gm5*gm7 + 2*g06*gm1*gm2*gm3*gm4*gm7*gm8 +
2*g08*gm1*gm2*gm3*gm4*gm7*gm8 + g011*gm2*gm3*gm4*gm5*gm7*gm8 + 2*gm1*gm2*gm3*gm4*gm5*gm7*gm8)
/
((2*CL*g01*g02*g03*g04*g05*g06 + 2*CL*g01*g02*g03*g04*g05*g08 + 2*CL*g01*g02*g03*g04*g06*g07 +
2*CL*g01*g02*g03*g05*g06*g07 + 2*CL*g01*g02*g03*g04*g07*g08 + 2*CL*g01*g02*g04*g05*g06*g07 +
2*CL*g01*g02*g03*g05*g07*g08 + 2*CL*g01*g03*g04*g05*g06*g07 + 2*CL*g01*g02*g04*g05*g07*g08 +
2*CL*g02*g03*g04*g05*g06*g07 + 2*CL*g01*g02*g03*g05*g06*g011 + 2*CL*g01*g03*g04*g05*g07*g08 +
2*CL*g02*g03*g04*g05*g07*g08 + 2*CL*g01*g02*g03*g05*g08*g011 + 2*CL*g01*g02*g03*g06*g07*g011 +
2*CL*g01*g03*g04*g05*g06*g011 + 2*CL*g01*g02*g03*g07*g08*g011 + 2*CL*g01*g02*g05*g06*g07*g011 +
2*CL*g01*g03*g04*g05*g08*g011 + 2*CL*g01*g03*g04*g06*g07*g011 + 2*CL*g01*g02*g05*g07*g08*g011 +
MATLAB Solution Continued 2:2*CL*g01*g03*g04*g07*g08*g011 + 2*CL*g01*g04*g05*g06*g07*g011 + 2*CL*g02*g03*g05*g06*g07*g011 +
2*CL*g01*g04*g05*g07*g08*g011 + 2*CL*g02*g03*g05*g07*g08*g011 + 2*CL*g03*g04*g05*g06*g07*g011 +
2*CL*g03*g04*g05*g07*g08*g011 + 2*CL*g01*g02*g03*g04*g06*gm5 + 2*CL*g01*g02*g03*g05*g06*gm4 +
2*CL*g01*g03*g04*g05*g06*gm2 + 2*CL*g01*g02*g03*g04*g05*gm8 + 2*CL*g01*g02*g03*g04*g06*gm7 +
2*CL*g01*g02*g03*g04*g08*gm5 + 2*CL*g01*g02*g03*g05*g08*gm4 + 2*CL*g01*g02*g03*g06*g07*gm4 +
2*CL*g01*g03*g04*g05*g08*gm2 + 2*CL*g01*g03*g04*g06*g07*gm2 + 2*CL*g01*g02*g03*g05*g06*gm7 +
2*CL*g01*g02*g03*g06*g07*gm5 + 2*CL*g01*g02*g05*g06*g07*gm3 + 2*CL*g02*g03*g05*g06*g07*gm1 +
2*CL*g01*g02*g03*g04*g07*gm8 + 2*CL*g01*g02*g03*g04*g08*gm7 + 2*CL*g01*g02*g03*g07*g08*gm4 +
2*CL*g01*g02*g04*g05*g06*gm7 + 2*CL*g01*g02*g04*g06*g07*gm5 + 2*CL*g01*g02*g05*g06*g07*gm4 +
2*CL*g01*g03*g04*g07*g08*gm2 + 2*CL*g01*g04*g05*g06*g07*gm2 + 2*CL*g01*g02*g03*g05*g07*gm8 +
2*CL*g01*g02*g03*g05*g08*gm7 + 2*CL*g01*g02*g03*g07*g08*gm5 + 2*CL*g01*g02*g05*g07*g08*gm3 +
2*CL*g01*g03*g04*g05*g06*gm7 + 2*CL*g01*g03*g04*g06*g07*gm5 + 2*CL*g01*g03*g05*g06*g07*gm4 +
2*CL*g01*g04*g05*g06*g07*gm3 + 2*CL*g02*g03*g05*g07*g08*gm1 + 2*CL*g03*g04*g05*g06*g07*gm1 +
2*CL*g01*g02*g04*g05*g07*gm8 + 2*CL*g01*g02*g04*g05*g08*gm7 + 2*CL*g01*g02*g04*g07*g08*gm5 +
2*CL*g01*g02*g05*g07*g08*gm4 + 2*CL*g01*g04*g05*g07*g08*gm2 + 2*CL*g02*g03*g04*g05*g06*gm7 +
2*CL*g02*g03*g04*g06*g07*gm5 + 2*CL*g02*g03*g05*g06*g07*gm4 + 2*CL*g02*g04*g05*g06*g07*gm3 +
2*CL*g03*g04*g05*g06*g07*gm2 + 2*CL*g01*g02*g03*g06*g011*gm5 + 2*CL*g01*g03*g04*g05*g07*gm8 +
2*CL*g01*g03*g04*g05*g08*gm7 + 2*CL*g01*g03*g04*g07*g08*gm5 + 2*CL*g01*g03*g05*g07*g08*gm4 +
2*CL*g01*g04*g05*g07*g08*gm3 + 2*CL*g03*g04*g05*g07*g08*gm1 + 2*CL*g02*g03*g04*g05*g07*gm8 +
2*CL*g02*g03*g04*g05*g08*gm7 + 2*CL*g02*g03*g04*g07*g08*gm5 + 2*CL*g02*g03*g05*g07*g08*gm4 +
2*CL*g02*g04*g05*g07*g08*gm3 + 2*CL*g03*g04*g05*g07*g08*gm2 + 2*CL*g01*g02*g03*g05*g011*gm8 +
2*CL*g01*g02*g03*g06*g011*gm7 + 2*CL*g01*g02*g03*g08*g011*gm5 + 2*CL*g01*g03*g04*g06*g011*gm5 +
2*CL*g01*g03*g05*g06*g011*gm4 + 2*CL*g01*g02*g03*g07*g011*gm8 + 2*CL*g01*g02*g03*g08*g011*gm7 +
2*CL*g01*g02*g05*g06*g011*gm7 + 2*CL*g01*g02*g06*g07*g011*gm5 + 2*CL*g01*g03*g04*g05*g011*gm8 +
2*CL*g01*g03*g04*g06*g011*gm7 + 2*CL*g01*g03*g04*g08*g011*gm5 + 2*CL*g01*g03*g05*g08*g011*gm4 +
2*CL*g01*g03*g06*g07*g011*gm4 + 2*CL*g01*g02*g05*g07*g011*gm8 + 2*CL*g01*g02*g05*g08*g011*gm7 +
2*CL*g01*g02*g07*g08*g011*gm5 + 2*CL*g01*g03*g04*g07*g011*gm8 + 2*CL*g01*g03*g04*g08*g011*gm7 +
2*CL*g01*g03*g07*g08*g011*gm4 + 2*CL*g01*g04*g05*g06*g011*gm7 + 2*CL*g01*g04*g06*g07*g011*gm5 +
2*CL*g01*g05*g06*g07*g011*gm4 + 2*CL*g02*g03*g05*g06*g011*gm7 + 2*CL*g02*g03*g06*g07*g011*gm5 +
2*CL*g02*g05*g06*g07*g011*gm3 + 2*CL*g01*g04*g05*g07*g011*gm8 + 2*CL*g01*g04*g05*g08*g011*gm7 +
2*CL*g01*g04*g07*g08*g011*gm5 + 2*CL*g01*g05*g07*g08*g011*gm4 + 2*CL*g02*g03*g05*g07*g011*gm8 +
2*CL*g02*g03*g05*g08*g011*gm7 + 2*CL*g02*g03*g07*g08*g011*gm5 + 2*CL*g02*g05*g07*g08*g011*gm3 +
2*CL*g03*g04*g05*g06*g011*gm7 + 2*CL*g03*g04*g06*g07*g011*gm5 + 2*CL*g03*g05*g06*g07*g011*gm4 +
2*CL*g04*g05*g06*g07*g011*gm3 + 2*CL*g03*g04*g05*g07*g011*gm8 + 2*CL*g03*g04*g05*g08*g011*gm7 +
2*CL*g03*g04*g07*g08*g011*gm5 + 2*CL*g03*g05*g07*g08*g011*gm4 + 2*CL*g04*g05*g07*g08*g011*gm3 +
2*CL*g01*g02*g03*g06*gm4*gm5 + 2*CL*g01*g03*g04*g06*gm2*gm5 + 2*CL*g01*g03*g05*g06*gm2*gm4 +
2*CL*g01*g02*g03*g04*gm5*gm8 + 2*CL*g01*g02*g03*g05*gm4*gm8 + 2*CL*g01*g02*g03*g06*gm4*gm7 +
2*CL*g01*g02*g03*g08*gm4*gm5 + 2*CL*g01*g03*g04*g05*gm2*gm8 + 2*CL*g01*g03*g04*g06*gm2*gm7 +
2*CL*g01*g03*g04*g08*gm2*gm5 + 2*CL*g01*g03*g05*g08*gm2*gm4 + 2*CL*g01*g03*g06*g07*gm2*gm4 +
2*CL*g01*g02*g03*g06*gm5*gm7 + 2*CL*g01*g02*g05*g06*gm3*gm7 + 2*CL*g01*g02*g06*g07*gm3*gm5 +
2*CL*g02*g03*g05*g06*gm1*gm7 + 2*CL*g02*g03*g06*g07*gm1*gm5 + 2*CL*g02*g05*g06*g07*gm1*gm3 +
2*CL*g01*g02*g03*g04*gm7*gm8 + 2*CL*g01*g02*g03*g07*gm4*gm8 + 2*CL*g01*g02*g03*g08*gm4*gm7 +
2*CL*g01*g02*g04*g06*gm5*gm7 + 2*CL*g01*g02*g05*g06*gm4*gm7 + 2*CL*g01*g02*g06*g07*gm4*gm5 +
2*CL*g01*g03*g04*g07*gm2*gm8 + 2*CL*g01*g03*g04*g08*gm2*gm7 + 2*CL*g01*g03*g07*g08*gm2*gm4 +
2*CL*g01*g04*g05*g06*gm2*gm7 + 2*CL*g01*g04*g06*g07*gm2*gm5 + 2*CL*g01*g05*g06*g07*gm2*gm4 +
2*CL*g01*g02*g03*g05*gm7*gm8 + 2*CL*g01*g02*g03*g07*gm5*gm8 + 2*CL*g01*g02*g03*g08*gm5*gm7 +
2*CL*g01*g02*g05*g07*gm3*gm8 + 2*CL*g01*g02*g05*g08*gm3*gm7 + 2*CL*g01*g02*g07*g08*gm3*gm5 +
2*CL*g01*g03*g04*g06*gm5*gm7 + 2*CL*g01*g03*g05*g06*gm4*gm7 + 2*CL*g01*g03*g06*g07*gm4*gm5 +
2*CL*g01*g04*g05*g06*gm3*gm7 + 2*CL*g01*g04*g06*g07*gm3*gm5 + 2*CL*g01*g05*g06*g07*gm3*gm4 +
2*CL*g02*g03*g05*g07*gm1*gm8 + 2*CL*g02*g03*g05*g08*gm1*gm7 + 2*CL*g02*g03*g07*g08*gm1*gm5 +
2*CL*g02*g05*g07*g08*gm1*gm3 + 2*CL*g03*g04*g05*g06*gm1*gm7 + 2*CL*g03*g04*g06*g07*gm1*gm5 +
2*CL*g03*g05*g06*g07*gm1*gm4 + 2*CL*g04*g05*g06*g07*gm1*gm3 + 2*CL*g01*g02*g04*g05*gm7*gm8 +
2*CL*g01*g02*g04*g07*gm5*gm8 + 2*CL*g01*g02*g04*g08*gm5*gm7 + 2*CL*g01*g02*g05*g07*gm4*gm8 +
2*CL*g01*g02*g05*g08*gm4*gm7 + 2*CL*g01*g02*g07*g08*gm4*gm5 + 2*CL*g01*g04*g05*g07*gm2*gm8 +
2*CL*g01*g04*g05*g08*gm2*gm7 + 2*CL*g01*g04*g07*g08*gm2*gm5 + 2*CL*g01*g05*g07*g08*gm2*gm4 +
2*CL*g02*g03*g04*g06*gm5*gm7 + 2*CL*g02*g03*g05*g06*gm4*gm7 + 2*CL*g02*g03*g06*g07*gm4*gm5 +
2*CL*g02*g04*g05*g06*gm3*gm7 + 2*CL*g02*g04*g06*g07*gm3*gm5 + 2*CL*g02*g05*g06*g07*gm3*gm4 +
2*CL*g03*g04*g05*g06*gm2*gm7 + 2*CL*g03*g04*g06*g07*gm2*gm5 + 2*CL*g03*g05*g06*g07*gm2*gm4 +
2*CL*g04*g05*g06*g07*gm2*gm3 + 2*CL*g01*g03*g04*g05*gm7*gm8 + 2*CL*g01*g03*g04*g07*gm5*gm8 +
2*CL*g01*g03*g04*g08*gm5*gm7 + 2*CL*g01*g03*g05*g07*gm4*gm8 + 2*CL*g01*g03*g05*g08*gm4*gm7 +
2*CL*g01*g03*g07*g08*gm4*gm5 + 2*CL*g01*g04*g05*g07*gm3*gm8 + 2*CL*g01*g04*g05*g08*gm3*gm7 +
2*CL*g01*g04*g07*g08*gm3*gm5 + 2*CL*g01*g05*g07*g08*gm3*gm4 + 2*CL*g03*g04*g05*g07*gm1*gm8 +
2*CL*g03*g04*g05*g08*gm1*gm7 + 2*CL*g03*g04*g07*g08*gm1*gm5 + 2*CL*g03*g05*g07*g08*gm1*gm4 +
2*CL*g04*g05*g07*g08*gm1*gm3 + 2*CL*g02*g03*g04*g05*gm7*gm8 + 2*CL*g02*g03*g04*g07*gm5*gm8 +
2*CL*g02*g03*g04*g08*gm5*gm7 + 2*CL*g02*g03*g05*g07*gm4*gm8 + 2*CL*g02*g03*g05*g08*gm4*gm7 +
2*CL*g02*g03*g07*g08*gm4*gm5 + 2*CL*g02*g04*g05*g07*gm3*gm8 + 2*CL*g02*g04*g05*g08*gm3*gm7 +
2*CL*g02*g04*g07*g08*gm3*gm5 + 2*CL*g02*g05*g07*g08*gm3*gm4 + 2*CL*g03*g04*g05*g07*gm2*gm8 +
2*CL*g03*g04*g05*g08*gm2*gm7 + 2*CL*g03*g04*g07*g08*gm2*gm5 + 2*CL*g03*g05*g07*g08*gm2*gm4 +
2*CL*g04*g05*g07*g08*gm2*gm3 + 2*CL*g01*g02*g03*g011*gm5*gm8 + 2*CL*g01*g03*g06*g011*gm4*gm5 +
2*CL*g01*g02*g03*g011*gm7*gm8 + 2*CL*g01*g02*g06*g011*gm5*gm7 + 2*CL*g01*g03*g04*g011*gm5*gm8 +
2*CL*g01*g03*g05*g011*gm4*gm8 + 2*CL*g01*g03*g06*g011*gm4*gm7 + 2*CL*g01*g03*g08*g011*gm4*gm5 +
MATLAB Solution Continued 3:2*CL*g01*g02*g05*g011*gm7*gm8 + 2*CL*g01*g02*g07*g011*gm5*gm8 + 2*CL*g01*g02*g08*g011*gm5*gm7 +
2*CL*g01*g03*g04*g011*gm7*gm8 + 2*CL*g01*g03*g07*g011*gm4*gm8 + 2*CL*g01*g03*g08*g011*gm4*gm7 +
2*CL*g01*g04*g06*g011*gm5*gm7 + 2*CL*g01*g05*g06*g011*gm4*gm7 + 2*CL*g01*g06*g07*g011*gm4*gm5 +
2*CL*g02*g03*g06*g011*gm5*gm7 + 2*CL*g02*g05*g06*g011*gm3*gm7 + 2*CL*g02*g06*g07*g011*gm3*gm5 +
2*CL*g01*g04*g05*g011*gm7*gm8 + 2*CL*g01*g04*g07*g011*gm5*gm8 + 2*CL*g01*g04*g08*g011*gm5*gm7 +
2*CL*g01*g05*g07*g011*gm4*gm8 + 2*CL*g01*g05*g08*g011*gm4*gm7 + 2*CL*g01*g07*g08*g011*gm4*gm5 +
2*CL*g02*g03*g05*g011*gm7*gm8 + 2*CL*g02*g03*g07*g011*gm5*gm8 + 2*CL*g02*g03*g08*g011*gm5*gm7 +
2*CL*g02*g05*g07*g011*gm3*gm8 + 2*CL*g02*g05*g08*g011*gm3*gm7 + 2*CL*g02*g07*g08*g011*gm3*gm5 +
2*CL*g03*g04*g06*g011*gm5*gm7 + 2*CL*g03*g05*g06*g011*gm4*gm7 + 2*CL*g03*g06*g07*g011*gm4*gm5 +
2*CL*g04*g05*g06*g011*gm3*gm7 + 2*CL*g04*g06*g07*g011*gm3*gm5 + 2*CL*g05*g06*g07*g011*gm3*gm4 +
2*CL*g03*g04*g05*g011*gm7*gm8 + 2*CL*g03*g04*g07*g011*gm5*gm8 + 2*CL*g03*g04*g08*g011*gm5*gm7 +
2*CL*g03*g05*g07*g011*gm4*gm8 + 2*CL*g03*g05*g08*g011*gm4*gm7 + 2*CL*g03*g07*g08*g011*gm4*gm5 +
2*CL*g04*g05*g07*g011*gm3*gm8 + 2*CL*g04*g05*g08*g011*gm3*gm7 + 2*CL*g04*g07*g08*g011*gm3*gm5 +
2*CL*g05*g07*g08*g011*gm3*gm4 + 2*CL*g01*g03*g06*gm2*gm4*gm5 + 2*CL*g01*g02*g03*gm4*gm5*gm8 +
2*CL*g01*g03*g04*gm2*gm5*gm8 + 2*CL*g01*g03*g05*gm2*gm4*gm8 + 2*CL*g01*g03*g06*gm2*gm4*gm7 +
2*CL*g01*g03*g08*gm2*gm4*gm5 + 2*CL*g01*g02*g06*gm3*gm5*gm7 + 2*CL*g02*g03*g06*gm1*gm5*gm7 +
2*CL*g02*g05*g06*gm1*gm3*gm7 + 2*CL*g02*g06*g07*gm1*gm3*gm5 + 2*CL*g01*g02*g03*gm4*gm7*gm8 +
2*CL*g01*g02*g06*gm4*gm5*gm7 + 2*CL*g01*g03*g04*gm2*gm7*gm8 + 2*CL*g01*g03*g07*gm2*gm4*gm8 +
2*CL*g01*g03*g08*gm2*gm4*gm7 + 2*CL*g01*g04*g06*gm2*gm5*gm7 + 2*CL*g01*g05*g06*gm2*gm4*gm7 +
2*CL*g01*g06*g07*gm2*gm4*gm5 + 2*CL*g01*g02*g03*gm5*gm7*gm8 + 2*CL*g01*g02*g05*gm3*gm7*gm8 +
2*CL*g01*g02*g07*gm3*gm5*gm8 + 2*CL*g01*g02*g08*gm3*gm5*gm7 + 2*CL*g01*g03*g06*gm4*gm5*gm7 +
2*CL*g01*g04*g06*gm3*gm5*gm7 + 2*CL*g01*g05*g06*gm3*gm4*gm7 + 2*CL*g01*g06*g07*gm3*gm4*gm5 +
2*CL*g02*g03*g05*gm1*gm7*gm8 + 2*CL*g02*g03*g07*gm1*gm5*gm8 + 2*CL*g02*g03*g08*gm1*gm5*gm7 +
2*CL*g02*g05*g07*gm1*gm3*gm8 + 2*CL*g02*g05*g08*gm1*gm3*gm7 + 2*CL*g02*g07*g08*gm1*gm3*gm5 +
2*CL*g03*g04*g06*gm1*gm5*gm7 + 2*CL*g03*g05*g06*gm1*gm4*gm7 + 2*CL*g03*g06*g07*gm1*gm4*gm5 +
2*CL*g04*g05*g06*gm1*gm3*gm7 + 2*CL*g04*g06*g07*gm1*gm3*gm5 + 2*CL*g05*g06*g07*gm1*gm3*gm4 +
2*CL*g01*g02*g04*gm5*gm7*gm8 + 2*CL*g01*g02*g05*gm4*gm7*gm8 + 2*CL*g01*g02*g07*gm4*gm5*gm8 +
2*CL*g01*g02*g08*gm4*gm5*gm7 + 2*CL*g01*g04*g05*gm2*gm7*gm8 + 2*CL*g01*g04*g07*gm2*gm5*gm8 +
2*CL*g01*g04*g08*gm2*gm5*gm7 + 2*CL*g01*g05*g07*gm2*gm4*gm8 + 2*CL*g01*g05*g08*gm2*gm4*gm7 +
2*CL*g01*g07*g08*gm2*gm4*gm5 + 2*CL*g02*g03*g06*gm4*gm5*gm7 + 2*CL*g02*g04*g06*gm3*gm5*gm7 +
2*CL*g02*g05*g06*gm3*gm4*gm7 + 2*CL*g02*g06*g07*gm3*gm4*gm5 + 2*CL*g03*g04*g06*gm2*gm5*gm7 +
2*CL*g03*g05*g06*gm2*gm4*gm7 + 2*CL*g03*g06*g07*gm2*gm4*gm5 + 2*CL*g04*g05*g06*gm2*gm3*gm7 +
2*CL*g04*g06*g07*gm2*gm3*gm5 + 2*CL*g05*g06*g07*gm2*gm3*gm4 + 2*CL*g01*g03*g04*gm5*gm7*gm8 +
2*CL*g01*g03*g05*gm4*gm7*gm8 + 2*CL*g01*g03*g07*gm4*gm5*gm8 + 2*CL*g01*g03*g08*gm4*gm5*gm7 +
2*CL*g01*g04*g05*gm3*gm7*gm8 + 2*CL*g01*g04*g07*gm3*gm5*gm8 + 2*CL*g01*g04*g08*gm3*gm5*gm7 +
2*CL*g01*g05*g07*gm3*gm4*gm8 + 2*CL*g01*g05*g08*gm3*gm4*gm7 + 2*CL*g01*g07*g08*gm3*gm4*gm5 +
2*CL*g03*g04*g05*gm1*gm7*gm8 + 2*CL*g03*g04*g07*gm1*gm5*gm8 + 2*CL*g03*g04*g08*gm1*gm5*gm7 +
2*CL*g03*g05*g07*gm1*gm4*gm8 + 2*CL*g03*g05*g08*gm1*gm4*gm7 + 2*CL*g03*g07*g08*gm1*gm4*gm5 +
2*CL*g04*g05*g07*gm1*gm3*gm8 + 2*CL*g04*g05*g08*gm1*gm3*gm7 + 2*CL*g04*g07*g08*gm1*gm3*gm5 +
2*CL*g05*g07*g08*gm1*gm3*gm4 + 2*CL*g02*g03*g04*gm5*gm7*gm8 + 2*CL*g02*g03*g05*gm4*gm7*gm8 +
2*CL*g02*g03*g07*gm4*gm5*gm8 + 2*CL*g02*g03*g08*gm4*gm5*gm7 + 2*CL*g02*g04*g05*gm3*gm7*gm8 +
2*CL*g02*g04*g07*gm3*gm5*gm8 + 2*CL*g02*g04*g08*gm3*gm5*gm7 + 2*CL*g02*g05*g07*gm3*gm4*gm8 +
2*CL*g02*g05*g08*gm3*gm4*gm7 + 2*CL*g02*g07*g08*gm3*gm4*gm5 + 2*CL*g03*g04*g05*gm2*gm7*gm8 +
2*CL*g03*g04*g07*gm2*gm5*gm8 + 2*CL*g03*g04*g08*gm2*gm5*gm7 + 2*CL*g03*g05*g07*gm2*gm4*gm8 +
2*CL*g03*g05*g08*gm2*gm4*gm7 + 2*CL*g03*g07*g08*gm2*gm4*gm5 + 2*CL*g04*g05*g07*gm2*gm3*gm8 +
2*CL*g04*g05*g08*gm2*gm3*gm7 + 2*CL*g04*g07*g08*gm2*gm3*gm5 + 2*CL*g05*g07*g08*gm2*gm3*gm4 +
2*CL*g01*g03*g011*gm4*gm5*gm8 + 2*CL*g01*g02*g011*gm5*gm7*gm8 + 2*CL*g01*g03*g011*gm4*gm7*gm8 +
2*CL*g01*g06*g011*gm4*gm5*gm7 + 2*CL*g02*g06*g011*gm3*gm5*gm7 + 2*CL*g01*g04*g011*gm5*gm7*gm8 +
2*CL*g01*g05*g011*gm4*gm7*gm8 + 2*CL*g01*g07*g011*gm4*gm5*gm8 + 2*CL*g01*g08*g011*gm4*gm5*gm7 +
2*CL*g02*g03*g011*gm5*gm7*gm8 + 2*CL*g02*g05*g011*gm3*gm7*gm8 + 2*CL*g02*g07*g011*gm3*gm5*gm8 +
2*CL*g02*g08*g011*gm3*gm5*gm7 + 2*CL*g03*g06*g011*gm4*gm5*gm7 + 2*CL*g04*g06*g011*gm3*gm5*gm7 +
2*CL*g05*g06*g011*gm3*gm4*gm7 + 2*CL*g06*g07*g011*gm3*gm4*gm5 + 2*CL*g03*g04*g011*gm5*gm7*gm8 +
2*CL*g03*g05*g011*gm4*gm7*gm8 + 2*CL*g03*g07*g011*gm4*gm5*gm8 + 2*CL*g03*g08*g011*gm4*gm5*gm7 +
2*CL*g04*g05*g011*gm3*gm7*gm8 + 2*CL*g04*g07*g011*gm3*gm5*gm8 + 2*CL*g04*g08*g011*gm3*gm5*gm7 +
2*CL*g05*g07*g011*gm3*gm4*gm8 + 2*CL*g05*g08*g011*gm3*gm4*gm7 + 2*CL*g07*g08*g011*gm3*gm4*gm5 +
2*CL*g01*g03*gm2*gm4*gm5*gm8 + 2*CL*g02*g06*gm1*gm3*gm5*gm7 + 2*CL*g01*g03*gm2*gm4*gm7*gm8 +
2*CL*g01*g06*gm2*gm4*gm5*gm7 + 2*CL*g01*g02*gm3*gm5*gm7*gm8 + 2*CL*g01*g06*gm3*gm4*gm5*gm7 +
2*CL*g02*g03*gm1*gm5*gm7*gm8 + 2*CL*g02*g05*gm1*gm3*gm7*gm8 + 2*CL*g02*g07*gm1*gm3*gm5*gm8 +
2*CL*g02*g08*gm1*gm3*gm5*gm7 + 2*CL*g03*g06*gm1*gm4*gm5*gm7 + 2*CL*g04*g06*gm1*gm3*gm5*gm7 +
2*CL*g05*g06*gm1*gm3*gm4*gm7 + 2*CL*g06*g07*gm1*gm3*gm4*gm5 + 2*CL*g01*g02*gm4*gm5*gm7*gm8 +
2*CL*g01*g04*gm2*gm5*gm7*gm8 + 2*CL*g01*g05*gm2*gm4*gm7*gm8 + 2*CL*g01*g07*gm2*gm4*gm5*gm8 +
2*CL*g01*g08*gm2*gm4*gm5*gm7 + 2*CL*g02*g06*gm3*gm4*gm5*gm7 + 2*CL*g03*g06*gm2*gm4*gm5*gm7 +
2*CL*g04*g06*gm2*gm3*gm5*gm7 + 2*CL*g05*g06*gm2*gm3*gm4*gm7 + 2*CL*g06*g07*gm2*gm3*gm4*gm5 +
2*CL*g01*g03*gm4*gm5*gm7*gm8 + 2*CL*g01*g04*gm3*gm5*gm7*gm8 + 2*CL*g01*g05*gm3*gm4*gm7*gm8 +
2*CL*g01*g07*gm3*gm4*gm5*gm8 + 2*CL*g01*g08*gm3*gm4*gm5*gm7 + 2*CL*g03*g04*gm1*gm5*gm7*gm8 +
2*CL*g03*g05*gm1*gm4*gm7*gm8 + 2*CL*g03*g07*gm1*gm4*gm5*gm8 + 2*CL*g03*g08*gm1*gm4*gm5*gm7 +
2*CL*g04*g05*gm1*gm3*gm7*gm8 + 2*CL*g04*g07*gm1*gm3*gm5*gm8 + 2*CL*g04*g08*gm1*gm3*gm5*gm7 +
2*CL*g05*g07*gm1*gm3*gm4*gm8 + 2*CL*g05*g08*gm1*gm3*gm4*gm7 + 2*CL*g07*g08*gm1*gm3*gm4*gm5 +
2*CL*g02*g03*gm4*gm5*gm7*gm8 + 2*CL*g02*g04*gm3*gm5*gm7*gm8 + 2*CL*g02*g05*gm3*gm4*gm7*gm8 +
2*CL*g02*g07*gm3*gm4*gm5*gm8 + 2*CL*g02*g08*gm3*gm4*gm5*gm7 + 2*CL*g03*g04*gm2*gm5*gm7*gm8 +
2*CL*g03*g05*gm2*gm4*gm7*gm8 + 2*CL*g03*g07*gm2*gm4*gm5*gm8 + 2*CL*g03*g08*gm2*gm4*gm5*gm7 +
MATLAB Solution Continued 4:2*CL*g04*g05*gm2*gm3*gm7*gm8 + 2*CL*g04*g07*gm2*gm3*gm5*gm8 + 2*CL*g04*g08*gm2*gm3*gm5*gm7 +
2*CL*g05*g07*gm2*gm3*gm4*gm8 + 2*CL*g05*g08*gm2*gm3*gm4*gm7 + 2*CL*g07*g08*gm2*gm3*gm4*gm5 +
2*CL*g01*g011*gm4*gm5*gm7*gm8 + 2*CL*g02*g011*gm3*gm5*gm7*gm8 + 2*CL*g06*g011*gm3*gm4*gm5*gm7 +
2*CL*g03*g011*gm4*gm5*gm7*gm8 + 2*CL*g04*g011*gm3*gm5*gm7*gm8 + 2*CL*g05*g011*gm3*gm4*gm7*gm8 +
2*CL*g07*g011*gm3*gm4*gm5*gm8 + 2*CL*g08*g011*gm3*gm4*gm5*gm7 + 2*CL*g02*gm1*gm3*gm5*gm7*gm8 +
2*CL*g06*gm1*gm3*gm4*gm5*gm7 + 2*CL*g01*gm2*gm4*gm5*gm7*gm8 + 2*CL*g06*gm2*gm3*gm4*gm5*gm7 +
2*CL*g01*gm3*gm4*gm5*gm7*gm8 + 2*CL*g03*gm1*gm4*gm5*gm7*gm8 + 2*CL*g04*gm1*gm3*gm5*gm7*gm8 +
2*CL*g05*gm1*gm3*gm4*gm7*gm8 + 2*CL*g07*gm1*gm3*gm4*gm5*gm8 + 2*CL*g08*gm1*gm3*gm4*gm5*gm7 +
2*CL*g02*gm3*gm4*gm5*gm7*gm8 + 2*CL*g03*gm2*gm4*gm5*gm7*gm8 + 2*CL*g04*gm2*gm3*gm5*gm7*gm8 +
2*CL*g05*gm2*gm3*gm4*gm7*gm8 + 2*CL*g07*gm2*gm3*gm4*gm5*gm8 + 2*CL*g08*gm2*gm3*gm4*gm5*gm7 +
2*CL*g011*gm3*gm4*gm5*gm7*gm8 + 2*CL*gm1*gm3*gm4*gm5*gm7*gm8 + 2*CL*gm2*gm3*gm4*gm5*gm7*gm8)*s +
(2*g01*g02*g03*g04*g07*gm8^2 + 2*g01*g02*g03*g04*gm7*gm8^2 + 2*g01*g02*g04*g07*gm3*gm8^2 +
2*g02*g03*g04*g07*gm1*gm8^2 + 2*g01*g02*g04*gm3*gm7*gm8^2 + 2*g02*g03*g04*gm1*gm7*gm8^2 +
2*g02*g04*g07*gm1*gm3*gm8^2 + 2*g02*g04*gm1*gm3*gm7*gm8^2 + 2*g01*g02*g03*g04*g05*g06*g07 +
2*g01*g02*g03*g04*g05*g06*g08 + 2*g01*g02*g03*g04*g05*g07*g08 + 2*g01*g02*g03*g04*g06*g07*g08 +
2*g01*g02*g03*g04*g05*g06*g011 + 2*g01*g02*g03*g05*g06*g07*g08 + 2*g01*g02*g04*g05*g06*g07*g08 +
2*g01*g02*g03*g04*g05*g08*g011 + 2*g01*g02*g03*g04*g06*g07*g011 + 2*g01*g03*g04*g05*g06*g07*g08
+ 2*g02*g03*g04*g05*g06*g07*g08 + 2*g01*g02*g03*g04*g07*g08*g011 +
2*g01*g02*g03*g05*g06*g08*g011 + 2*g01*g02*g04*g05*g06*g07*g011 + 2*g01*g02*g03*g06*g07*g08*g011
+ 2*g01*g02*g04*g05*g07*g08*g011 + 2*g01*g03*g04*g05*g06*g08*g011 +
2*g02*g03*g04*g05*g06*g07*g011 + 2*g01*g02*g05*g06*g07*g08*g011 + 2*g01*g03*g04*g06*g07*g08*g011
+ 2*g02*g03*g04*g05*g07*g08*g011 + 2*g01*g04*g05*g06*g07*g08*g011 +
2*g02*g03*g05*g06*g07*g08*g011 + 2*g03*g04*g05*g06*g07*g08*g011 + 2*g01*g02*g03*g04*g05*g06*gm7
+ 2*g01*g02*g03*g04*g06*g07*gm5 + 2*g01*g02*g04*g05*g06*g07*gm3 + 2*g02*g03*g04*g05*g06*g07*gm1
+ 2*g01*g02*g03*g04*g05*g06*gm8 + 2*g01*g02*g03*g04*g06*g08*gm5 + 2*g01*g02*g03*g05*g06*g08*gm4
+ 2*g01*g03*g04*g05*g06*g08*gm2 + 2*g01*g02*g03*g04*g05*g07*gm8 + 2*g01*g02*g03*g04*g05*g08*gm7
+ 2*g01*g02*g03*g04*g07*g08*gm5 + 2*g01*g02*g04*g05*g07*g08*gm3 + 2*g02*g03*g04*g05*g07*g08*gm1
+ 2*g01*g02*g03*g04*g06*g07*gm8 + 2*g01*g02*g03*g04*g06*g08*gm7 + 2*g01*g02*g03*g06*g07*g08*gm4
+ 2*g01*g03*g04*g06*g07*g08*gm2 + 2*g01*g02*g03*g04*g06*g011*gm5 + 2*g01*g02*g03*g05*g06*g08*gm7
+ 2*g01*g02*g03*g06*g07*g08*gm5 + 2*g01*g02*g05*g06*g07*g08*gm3 + 2*g02*g03*g05*g06*g07*g08*gm1
+ 2*g01*g02*g03*g04*g07*g08*gm8 + 2*g01*g02*g04*g05*g06*g08*gm7 + 2*g01*g02*g04*g06*g07*g08*gm5
+ 2*g01*g02*g05*g06*g07*g08*gm4 + 2*g01*g04*g05*g06*g07*g08*gm2 + 2*g01*g02*g03*g04*g05*g011*gm8
+ 2*g01*g02*g03*g04*g06*g011*gm7 + 2*g01*g02*g03*g04*g08*g011*gm5 +
2*g01*g03*g04*g05*g06*g08*gm7 + 2*g01*g03*g04*g06*g07*g08*gm5 + 2*g01*g03*g05*g06*g07*g08*gm4 +
2*g01*g04*g05*g06*g07*g08*gm3 + 2*g03*g04*g05*g06*g07*g08*gm1 + 2*g02*g03*g04*g05*g06*g08*gm7 +
2*g02*g03*g04*g06*g07*g08*gm5 + 2*g02*g03*g05*g06*g07*g08*gm4 + 2*g02*g04*g05*g06*g07*g08*gm3 +
2*g03*g04*g05*g06*g07*g08*gm2 + 2*g01*g02*g03*g04*g07*g011*gm8 + 2*g01*g02*g03*g04*g08*g011*gm7
+ 2*g01*g02*g03*g06*g08*g011*gm5 + 2*g01*g02*g04*g05*g06*g011*gm7 +
2*g01*g02*g04*g06*g07*g011*gm5 + 2*g01*g02*g03*g06*g08*g011*gm7 + 2*g01*g02*g04*g05*g07*g011*gm8
+ 2*g01*g02*g04*g05*g08*g011*gm7 + 2*g01*g02*g04*g07*g08*g011*gm5 +
2*g01*g03*g04*g06*g08*g011*gm5 + 2*g01*g03*g05*g06*g08*g011*gm4 + 2*g02*g03*g04*g05*g06*g011*gm7
+ 2*g02*g03*g04*g06*g07*g011*gm5 + 2*g02*g04*g05*g06*g07*g011*gm3 +
2*g01*g02*g05*g06*g08*g011*gm7 + 2*g01*g02*g06*g07*g08*g011*gm5 + 2*g01*g03*g04*g06*g08*g011*gm7
+ 2*g01*g03*g06*g07*g08*g011*gm4 + 2*g02*g03*g04*g05*g07*g011*gm8 +
2*g02*g03*g04*g05*g08*g011*gm7 + 2*g02*g03*g04*g07*g08*g011*gm5 + 2*g02*g04*g05*g07*g08*g011*gm3
+ 2*g01*g04*g05*g06*g08*g011*gm7 + 2*g01*g04*g06*g07*g08*g011*gm5 +
2*g01*g05*g06*g07*g08*g011*gm4 + 2*g02*g03*g05*g06*g08*g011*gm7 + 2*g02*g03*g06*g07*g08*g011*gm5
+ 2*g02*g05*g06*g07*g08*g011*gm3 + 2*g03*g04*g05*g06*g08*g011*gm7 +
2*g03*g04*g06*g07*g08*g011*gm5 + 2*g03*g05*g06*g07*g08*g011*gm4 + 2*g04*g05*g06*g07*g08*g011*gm3
+ 2*g01*g02*g03*g04*g06*gm5*gm7 + 2*g01*g02*g04*g05*g06*gm3*gm7 + 2*g01*g02*g04*g06*g07*gm3*gm5
+ 2*g02*g03*g04*g05*g06*gm1*gm7 + 2*g02*g03*g04*g06*g07*gm1*gm5 + 2*g02*g04*g05*g06*g07*gm1*gm3
+ 2*g01*g02*g03*g04*g06*gm5*gm8 + 2*g01*g02*g03*g06*g08*gm4*gm5 + 2*g01*g02*g04*g05*g06*gm3*gm8
+ 2*g01*g03*g04*g06*g08*gm2*gm5 + 2*g01*g03*g05*g06*g08*gm2*gm4 + 2*g02*g03*g04*g05*g06*gm1*gm8
+ 2*g01*g02*g03*g04*g05*gm7*gm8 + 2*g01*g02*g03*g04*g07*gm5*gm8 + 2*g01*g02*g03*g04*g08*gm5*gm7
+ 2*g01*g02*g04*g05*g07*gm3*gm8 + 2*g01*g02*g04*g05*g08*gm3*gm7 + 2*g01*g02*g04*g07*g08*gm3*gm5
+ 2*g02*g03*g04*g05*g07*gm1*gm8 + 2*g02*g03*g04*g05*g08*gm1*gm7 + 2*g02*g03*g04*g07*g08*gm1*gm5
+ 2*g02*g04*g05*g07*g08*gm1*gm3 + 2*g01*g02*g03*g04*g06*gm7*gm8 + 2*g01*g02*g03*g06*g08*gm4*gm7
+ 2*g01*g02*g04*g06*g07*gm3*gm8 + 2*g01*g03*g04*g06*g08*gm2*gm7 + 2*g01*g03*g06*g07*g08*gm2*gm4
+ 2*g02*g03*g04*g06*g07*gm1*gm8 + 2*g01*g02*g03*g06*g08*gm5*gm7 + 2*g01*g02*g05*g06*g08*gm3*gm7
+ 2*g01*g02*g06*g07*g08*gm3*gm5 + 2*g02*g03*g05*g06*g08*gm1*gm7 + 2*g02*g03*g06*g07*g08*gm1*gm5
+ 2*g02*g05*g06*g07*g08*gm1*gm3 + 2*g01*g02*g03*g04*g08*gm7*gm8 + 2*g01*g02*g04*g06*g08*gm5*gm7
+ 2*g01*g02*g04*g07*g08*gm3*gm8 + 2*g01*g02*g05*g06*g08*gm4*gm7 + 2*g01*g02*g06*g07*g08*gm4*gm5
+ 2*g01*g04*g05*g06*g08*gm2*gm7 + 2*g01*g04*g06*g07*g08*gm2*gm5 + 2*g01*g05*g06*g07*g08*gm2*gm4
+ 2*g02*g03*g04*g07*g08*gm1*gm8 + 2*g01*g02*g03*g04*g011*gm5*gm8 + 2*g01*g03*g04*g06*g08*gm5*gm7
+ 2*g01*g03*g05*g06*g08*gm4*gm7 + 2*g01*g03*g06*g07*g08*gm4*gm5 + 2*g01*g04*g05*g06*g08*gm3*gm7
+ 2*g01*g04*g06*g07*g08*gm3*gm5 + 2*g01*g05*g06*g07*g08*gm3*gm4 + 2*g03*g04*g05*g06*g08*gm1*gm7
+ 2*g03*g04*g06*g07*g08*gm1*gm5 + 2*g03*g05*g06*g07*g08*gm1*gm4 + 2*g04*g05*g06*g07*g08*gm1*gm3
+ 2*g02*g03*g04*g06*g08*gm5*gm7 + 2*g02*g03*g05*g06*g08*gm4*gm7 + 2*g02*g03*g06*g07*g08*gm4*gm5
+ 2*g02*g04*g05*g06*g08*gm3*gm7 + 2*g02*g04*g06*g07*g08*gm3*gm5 + 2*g02*g05*g06*g07*g08*gm3*gm4
+ 2*g03*g04*g05*g06*g08*gm2*gm7 + 2*g03*g04*g06*g07*g08*gm2*gm5 + 2*g03*g05*g06*g07*g08*gm2*gm4
+ 2*g04*g05*g06*g07*g08*gm2*gm3 + 2*g01*g02*g03*g04*g011*gm7*gm8 +
MATLAB Solution Continued 5:2*g01*g02*g04*g06*g011*gm5*gm7 + 2*g01*g02*g04*g05*g011*gm7*gm8 + 2*g01*g02*g04*g07*g011*gm5*gm8
+ 2*g01*g02*g04*g08*g011*gm5*gm7 + 2*g01*g03*g06*g08*g011*gm4*gm5 +
2*g02*g03*g04*g06*g011*gm5*gm7 + 2*g02*g04*g05*g06*g011*gm3*gm7 + 2*g02*g04*g06*g07*g011*gm3*gm5
+ 2*g01*g02*g06*g08*g011*gm5*gm7 + 2*g01*g03*g06*g08*g011*gm4*gm7 +
2*g02*g03*g04*g05*g011*gm7*gm8 + 2*g02*g03*g04*g07*g011*gm5*gm8 + 2*g02*g03*g04*g08*g011*gm5*gm7
+ 2*g02*g04*g05*g07*g011*gm3*gm8 + 2*g02*g04*g05*g08*g011*gm3*gm7 +
2*g02*g04*g07*g08*g011*gm3*gm5 + 2*g01*g04*g06*g08*g011*gm5*gm7 + 2*g01*g05*g06*g08*g011*gm4*gm7
+ 2*g01*g06*g07*g08*g011*gm4*gm5 + 2*g02*g03*g06*g08*g011*gm5*gm7 +
2*g02*g05*g06*g08*g011*gm3*gm7 + 2*g02*g06*g07*g08*g011*gm3*gm5 + 2*g03*g04*g06*g08*g011*gm5*gm7
+ 2*g03*g05*g06*g08*g011*gm4*gm7 + 2*g03*g06*g07*g08*g011*gm4*gm5 +
2*g04*g05*g06*g08*g011*gm3*gm7 + 2*g04*g06*g07*g08*g011*gm3*gm5 + 2*g05*g06*g07*g08*g011*gm3*gm4
+ 2*g01*g02*g04*g06*gm3*gm5*gm7 + 2*g02*g03*g04*g06*gm1*gm5*gm7 + 2*g02*g04*g05*g06*gm1*gm3*gm7
+ 2*g02*g04*g06*g07*gm1*gm3*gm5 + 2*g01*g02*g04*g06*gm3*gm5*gm8 + 2*g01*g03*g06*g08*gm2*gm4*gm5
+ 2*g02*g03*g04*g06*gm1*gm5*gm8 + 2*g02*g04*g05*g06*gm1*gm3*gm8 + 2*g01*g02*g03*g04*gm5*gm7*gm8
+ 2*g01*g02*g04*g05*gm3*gm7*gm8 + 2*g01*g02*g04*g07*gm3*gm5*gm8 + 2*g01*g02*g04*g08*gm3*gm5*gm7
+ 2*g02*g03*g04*g05*gm1*gm7*gm8 + 2*g02*g03*g04*g07*gm1*gm5*gm8 + 2*g02*g03*g04*g08*gm1*gm5*gm7
+ 2*g02*g04*g05*g07*gm1*gm3*gm8 + 2*g02*g04*g05*g08*gm1*gm3*gm7 + 2*g02*g04*g07*g08*gm1*gm3*gm5
+ 2*g01*g02*g04*g06*gm3*gm7*gm8 + 2*g01*g03*g06*g08*gm2*gm4*gm7 + 2*g02*g03*g04*g06*gm1*gm7*gm8
+ 2*g02*g04*g06*g07*gm1*gm3*gm8 + 2*g01*g02*g06*g08*gm3*gm5*gm7 + 2*g02*g03*g06*g08*gm1*gm5*gm7
+ 2*g02*g05*g06*g08*gm1*gm3*gm7 + 2*g02*g06*g07*g08*gm1*gm3*gm5 + 2*g01*g02*g04*g08*gm3*gm7*gm8
+ 2*g01*g02*g06*g08*gm4*gm5*gm7 + 2*g01*g04*g06*g08*gm2*gm5*gm7 + 2*g01*g05*g06*g08*gm2*gm4*gm7
+ 2*g01*g06*g07*g08*gm2*gm4*gm5 + 2*g02*g03*g04*g08*gm1*gm7*gm8 + 2*g02*g04*g07*g08*gm1*gm3*gm8
+ 2*g01*g03*g06*g08*gm4*gm5*gm7 + 2*g01*g04*g06*g08*gm3*gm5*gm7 + 2*g01*g05*g06*g08*gm3*gm4*gm7
+ 2*g01*g06*g07*g08*gm3*gm4*gm5 + 2*g03*g04*g06*g08*gm1*gm5*gm7 + 2*g03*g05*g06*g08*gm1*gm4*gm7
+ 2*g03*g06*g07*g08*gm1*gm4*gm5 + 2*g04*g05*g06*g08*gm1*gm3*gm7 + 2*g04*g06*g07*g08*gm1*gm3*gm5
+ 2*g05*g06*g07*g08*gm1*gm3*gm4 + 2*g02*g03*g06*g08*gm4*gm5*gm7 + 2*g02*g04*g06*g08*gm3*gm5*gm7
+ 2*g02*g05*g06*g08*gm3*gm4*gm7 + 2*g02*g06*g07*g08*gm3*gm4*gm5 + 2*g03*g04*g06*g08*gm2*gm5*gm7
+ 2*g03*g05*g06*g08*gm2*gm4*gm7 + 2*g03*g06*g07*g08*gm2*gm4*gm5 + 2*g04*g05*g06*g08*gm2*gm3*gm7
+ 2*g04*g06*g07*g08*gm2*gm3*gm5 + 2*g05*g06*g07*g08*gm2*gm3*gm4 + 2*g01*g02*g04*g011*gm5*gm7*gm8
+ 2*g02*g04*g06*g011*gm3*gm5*gm7 + 2*g02*g03*g04*g011*gm5*gm7*gm8 +
2*g02*g04*g05*g011*gm3*gm7*gm8 + 2*g02*g04*g07*g011*gm3*gm5*gm8 + 2*g02*g04*g08*g011*gm3*gm5*gm7
+ 2*g01*g06*g08*g011*gm4*gm5*gm7 + 2*g02*g06*g08*g011*gm3*gm5*gm7 +
2*g03*g06*g08*g011*gm4*gm5*gm7 + 2*g04*g06*g08*g011*gm3*gm5*gm7 + 2*g05*g06*g08*g011*gm3*gm4*gm7
+ 2*g06*g07*g08*g011*gm3*gm4*gm5 + 2*g02*g04*g06*gm1*gm3*gm5*gm7 + 2*g02*g04*g06*gm1*gm3*gm5*gm8
+ 2*g01*g02*g04*gm3*gm5*gm7*gm8 + 2*g02*g03*g04*gm1*gm5*gm7*gm8 + 2*g02*g04*g05*gm1*gm3*gm7*gm8
+ 2*g02*g04*g07*gm1*gm3*gm5*gm8 + 2*g02*g04*g08*gm1*gm3*gm5*gm7 + 2*g02*g04*g06*gm1*gm3*gm7*gm8
+ 2*g02*g06*g08*gm1*gm3*gm5*gm7 + 2*g01*g06*g08*gm2*gm4*gm5*gm7 + 2*g02*g04*g08*gm1*gm3*gm7*gm8
+ 2*g01*g06*g08*gm3*gm4*gm5*gm7 + 2*g03*g06*g08*gm1*gm4*gm5*gm7 + 2*g04*g06*g08*gm1*gm3*gm5*gm7
+ 2*g05*g06*g08*gm1*gm3*gm4*gm7 + 2*g06*g07*g08*gm1*gm3*gm4*gm5 + 2*g02*g06*g08*gm3*gm4*gm5*gm7
+ 2*g03*g06*g08*gm2*gm4*gm5*gm7 + 2*g04*g06*g08*gm2*gm3*gm5*gm7 + 2*g05*g06*g08*gm2*gm3*gm4*gm7
+ 2*g06*g07*g08*gm2*gm3*gm4*gm5 + 2*g02*g04*g011*gm3*gm5*gm7*gm8 +
2*g06*g08*g011*gm3*gm4*gm5*gm7 + 2*g02*g04*gm1*gm3*gm5*gm7*gm8 + 2*g06*g08*gm1*gm3*gm4*gm5*gm7 +
2*g06*g08*gm2*gm3*gm4*gm5*gm7))
• Difference Mode Gain has only approximately 1100 product terms• Difference Mode Gain has approximately 7700 small-signal parameters in expression
• This does not even include the common-mode gain expression !
• Extremely difficult to get insight into how this relatively simple circuit performs
from this solution
VSS
VB5
VINVIN
M1M2
M3 M4
M5
M7
M6
M8
VB3
VOUT
CL
M11M12
IB
IT
VDD
Current Mirror Bias
VDD
Telescopic Cascode Op Amp with Mirror-connected Counterpart Circuit
• Previous analysis obtained almost by inspection• Gain expressions were real simple• Gain expressions provide major insight into operation• Some assumptions were made to simplify analysis
⁻ Vac=0 at “approximate axis of symmetry”⁻ Matched left and right side transistors⁻ Current mirror used to mirror left-side current to right side
How much more involved would an exact analysis be ?Would an exact analysis provide additional insight ?
Where this started
VSS
VB5
VINVIN
M1M2
M3 M4
M5
M7
M6
M8
VB3
VOUT
CL
M11M12
IB
IT
VDD
Current Mirror Bias
VDD
Telescopic Cascode Op Amp with Mirror-connected Counterpart Circuit
• Some assumptions were made to simplify analysis⁻ Vac=0 at “approximate axis of symmetry”⁻ Matched left and right side transistors⁻ Current mirror used to mirror left-side current to right side
Where this started
• Simplified Difference Mode Gain has 4 product terms• Simplified Difference Mode Gain has 12 small-signal parameters in expression
m1d
o3 o7L o1 o5
m3 m7
-gA s =
g gsC g + g
g g
How many product terms are present in the simplified analysis?
How many small-signal parameters are in simplified expression?
m7 m1 m3d
L m7 m3 m7 o3 o1 m3 o5 o7
-g g gA s =
sC g g g g g + g g g
• Difference Mode Gain has only approximately 1100 product terms• Difference Mode Gain has approximately 7700 small-signal parameters in expression
How important is it to develop good approximate analysis methods for an op amp of this complexity?
And many useful op amp circuits will have much more complexity !!
Will you impress your boss if you use an “exact” analysis?
52
Are there other high
output impedance
circuits that can be
used as quarter
circuits?
L
M1
L
21
21
M1VO
2C
GGB
C
GGBW
GG2
GA
53
Are there other high output impedance circuits that can be used
as quarter circuits ?
Regulated cascode
circuits have the high
output impedance
property
54
M1
M3
-A
VIN
VOUT
High output impedance quarter-circuits
Regulated Cascode Amplifier
or “Gain Boosted Cascode”
Quarter Circuit
• A is usually a simple amplifier, often the reference op amp with + terminal
connected to the desired quiescent voltage
• Assume biased with a dc current source (not shown) at drain of M3
55
go1gM1V1V1
go3gM3V2V2
VIN
VOUT
CL
-A VX
-A
M1
VIN
M3
VOUT
CL
Analysis of Regulated Cascode Amplifier
VX and V2 can be easily eliminated from these 3 equations
Background
OUT o3 L m3 2 X o3
X o1 o3 m1 IN m3 2 OUT o3
2 X X
V g +sC +g V =V g
V g +g +g V -g V =V g
V +V =-AV
56
-A
M1
VIN
M2
VOUT
CL
Analysis of Regulated Cascode AmplifierBackground
m1 o3 m3 m1 m3OUT m1
o1 o3IN L m3 o1 o3L o1 o3 m3 o1 o3L
m3
g g g 1 A g g 1 AV g
g gV sC g 1 A g gsC g g g 1 A g g sCg 1 A
for A large: gMEQ
gOEQ
OUT o3 L m3 2 X o3
X o1 o3 m1 IN m3 2 OUT o3
2 X X
V g +sC +g V =V g
V g +g +g V -g V =V g
V +V =-AV
OUT o3 L m3 X X o3
X o1 o3 m1 IN m3 X OUT o3
V g +sC -g V 1 =V g
V g +g +g V +g V 1 =V g
A
A
1
OUT m1
IN o3L o1
m3
V g
V gsC g
g A
57
High output impedance quarter-circuits
Regulated Cascode Amplifier
or “Gain Boosted Cascode”
Based upon small-signal analysis it appears that the
output conductance has been decreased even more!
Same GB as for previous two circuits
IDB1
M1
M3
-A
VIN
VOUT
CL
VSS
1
1o3o1
m3
gg
g A
OEQ
mEQ m
g
g g
m1V
o3L o1
m3
gA
gsC g
g A
m3m1O
o1 o3
g AgA
g g
m1
L
gGB
C
Must verify improvement in gain in
practical parameter domain !!
Verification will show predicted improvements
58
Gain-Boosted Telescopic Cascode Op Amp
M1
M3
-A
VIN
VOUT
Needs CMFB Circuit for Vb1
Either single-ended or differential outputs
Can connect counterpart as current mirror to eliminate CMFB
Use differential op amp to facilitate biasing of cascode device
VDD
V OU
T
CL
VB2
VB3
V S
S
VB5 M 1
1
VB1
A1A2
A3A4
IT
VINVIN
M1M2
M3 M4
M5
M7
M6
M8
59
Gain-Boosted Telescopic Cascode Op AmpV
DD
VOUT
CL
VB2
VB3
VSS
VB5 M
11
VB1
A1
A2
A3
A4
IT
VIN
VINM
1M
2
M3 M
4
M5
M7
M6
M8
Single-ended operation
gOQC =
gOCC =
gmQC =
60
Gain-Boosted Telescopic Cascode Op Amp
m1
oo3 o7
o1 o5
1 m3 3 m7
g-
2A =g g
g + gA g A g
This is modestly less efficient at
generating GB because now power is
consumed in both the cascode
devices and the boosting amplifier
VDD
V OU
T
CL
VB2
VB3
V S
S
VB5 M 1
1
VB1
A1A2
A3A4
IT
VINVIN
M1M2
M3 M4
M5
M7
M6
M8
m1
L
gGB
2C
61
Gain-Boosted Telescopic Cascode Op Amp
m1
L
gGB =
C
m1o
o3 o7o1 o5
1 m3 3 m7
-gA =
g gg + g
A g A g
This is modestly less efficient at
generating GB because now power is
consumed in both the cascode
devices and the boosting amplifier
VDD
V OU
T
CL
VB2
VB3
V S
S
VB5 M 1
1
A1A2
A3A4
IT
VINVIN
M1M2
M3 M4
M5
M7
M6
M8
Elimination of need for CMFB Circuit
62
Gain-Boosted Telescopic Cascode Op Amp
VDD
CL
VB2
VB3
V S
S
VB5 M
11
A1A2
A3A4
IT
VINVIN
M1M2
M3 M4
M5
M7
M6
M8
VDSAT
VOUT
VDSAT
VDSAT
VDSAT
VDSAT
A minimum of 5 VDSAT drops
between VDD and VSS
Signal Swing and Power Supply Limitations
This establishes a lower bound
on VDD-VSS and it will be reduced
by the p-p signal swing on the
output
63
Gain-Boosted Telescopic Cascode Op Amp
VDD
V OU
T
CL
VB2
VB3
V S
S
VB5 M 1
1
A1A2
A3A4
IT
VINVIN
M1M2
M3 M4
M5
M7
M6
M8
Advantages:
Significant increase in dc gain
Limitations:
:• Signal swing (4VDSAT+VT between VDD and VSS)
• Reduction in GB power efficiency
- some current required to bias “A” amplifiers
• -additional pole in “A” amplifier -may add requirements for some compensation
• Area Overhead for 4 transistors and 4 amplifiers-actually minor concern since performance will usually
justify these resources
(with or w/o current mirror counterpart circuits)
64
Are there other useful high output impedance
circuits that can be used for the quarter circuit?
V1G M1V1 G 1
V1G M1 G 1
G2
CL
2
Vd
Vo++
1
0
1 2
1 2
1
2
2
MV
L
M
L
GA
G G
G GBW
C
GGB
C
65
What circuit is this?
VSS
CL
M3
M1
IDB
VDD
VBB
VOUT
VIN
Cascode Amplifier
• Cascode Amplifier– Often termed a “Folded Cascode Amplifier”
– Same small-signal performance as other
– VOUT swing VDSAt1-VDSAT2 could be small or negative
– But a biasing problem !!
IB1
M1
M3
VOUT
VBB
VIN
VSS
CL
66
Biased Folded Cascode Amplifier
IB1
M1
M3
VOUT
VBB
VIN
VSS
Folded Cascode Amplifier
VDD
VIN
M1
M3V
B1IB1
IB2 V
OUT
VSS
Biased Folded Cascode
67
Implementation of Biased Folded
Cascode Amplifier?
VDD
VIN
M1
M3 M
5
VB1 V
B3
Biased Folded CascodeImplementation of Biased
Folded Cascode
VDD
VIN
M1
M3V
B1IB1
IB2 V
OUT
VSS
68
End of Lecture 9