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Politecnico di Torino - ICT School
Analog and Telecommunication Electronics
B3 - Using nonlinearity
» Tuned amplifier » Frequency multiplier » Gain compressor » Adding feedback
AY 2015-16
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Lesson B3: using nonlinearity
• Reducing the effects of nonlinearity– Tuned amplifiers– Large signal gain Gm(x)– Re feedback– Gain stabilization
• Exploiting nonlinearity– Dynamic compressors– Frequency multipliers
• Text reference:– Elettronica per Telecom.: sect. 1.2 Transistori fuori linearità
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Nonlinearity: fight or exploit ?
• We get: – Distortion– Harmonics – Variable gain
• Remove harmonics: tuned circuits
• Keep harmonics: frequency multipliers
• Stabilize the gain: negative feedback
• Use gain variation: compressor, VGA, mixers
• Sine oscillators:– Use gain change to get |Aβ| = 1
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Limit the effects of nonlinearity
• Negative feedback– OpAmp or OpAmp-like with feedback– Add feedback to transistor amplifiers
(Emitter resistance)» Reduce actual signal amplitude on the nonlinear element (pn
junction)
• Same effect for any frequency
• Suitable for wideband amplifiers
• No problem for fully integrated circuits
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Reduce harmonics and distorsion
• Tuned circuit at the output: ZC(ω)– Gain: |AV| ZC(ω)/ZE(ω)
• Suitable for narrowband amplifiers– Can attenuate the harmonics (and other unwanted signals)
– TX output stage (PA)» Remove unwanted components
– RX front end amplifiers (LNA)» Remove unwanted (outband) signals» Remove noise
• Fully integrated amplifiers low L C values– Tuned circuis feasible for F > K x 100 MHz
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Tuned amplifiers
LNA (low noise amplifier)
IF amplif.(tuned amplifiers)
PA (power amplifier)
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fi2 = fi1 – fO2
Dual-conversion heterodyne receiver
Input RF filterFirst IF:High easy image removal Second IF (IF2)Low Simple channel filter
Tuning by shifting O1 (or O2)
WidebandLNA + filter
X
O1
DEM.Va
IF1 filter +Amplif.
f
fa fO1fi1 = fa – fO1
X
O2IF2 filter +Amplif.
ffO2fi1 fi1b
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LRC tuned circuits
• Resonance: o
• Damping:
• Quality factor: Q = 1/2 • Attenuation:
k1kQX
k
X
logω
|z()|
Q
O kO
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Tuned amplifiers
• IC depends only on VBE
IC
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Tuned amplifiers
• VO depends on IC (VBE) and ZC ()
In this example O = I
VO
IC
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Output spectrum
• Harmonic contents of collector current Ic– IC current spectrum
depends only on Vi amplitude
• Effects of LC on Vu– Vu spectrum depends also from Zc, that is the resonator Q– add (in dB) the level caused by nonlinearity with resonant circuit
attenuation X– X depends from
frequency offset and quality factor Q
k
1kZ
Z kQXi
i
I
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Examples: fixed Q, variable Vi
Harmonic content of Ic depends only on input signal levelThe tuned circuit Q factor modifies the harmonic content of Vu
|Zc|, Q = 200(fixed)
Ic(ω)For Vi 5 …200 mVp
Vu(ω)
Vi = 5mV Vi = 20mV Vi = 200mV
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Examples: variable Q, fixed Vi
Harmonic content of Ic depends only on input signal levelThe tuned circuit Q factor modifies the harmonic content of Vu
|Zc|, Q = 50, 200, 500
Ic(ω) for Vi = 200 mVp(fixed)
Vu(ω)
Q = 50 Q = 200 Q = 500
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Example: tuned amplifier design
• Functional parameters:– Input signal level– Gain– Spectral purity– Power and efficiency
• Circuit parameters– Collector current IC (= IE = I)– Resonant circuit Q
• Exercise B3-a– From signal level and Q, compute output spectrum– Compute the Q required to get a given spectral purity
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Lesson A4: how to use nonlinearity
• Reducing the effects of nonlinearity– Tuned amplifiers– Gain stabilization
• Exploiting nonlinearity– Dynamic compressors– Frequency multipliers
• Sine oscillators– Positive feedback amplifiers– Negative transconductance
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Large-signal gain
• Input signal
• Small signal (linear model)
• Large signal (slide B2-12) (only fundamental component)
• Introducing large signal transconductance: Gm(x)(gain for the fundamental)
i Tv (t) x V cos t
o C m i
1m
T 0
v (t) R G (x)v (t)
I (x)IG (x) 2x V I (x)
1o C i
T 0
I (x)Iv (t) R 2 v (t)x V I (x)
o C m iv (t) R g v (t)
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Gm(x)
• Very low-level input signal (x 0)
– Gm(x)/gm = 1 (small signal, linear)
• As input level increases,
– Gm (x)/gm decreases (less gain)
• Steep slope for x = 3 … 6… compression
Small signal
Compression
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Verification for small signal
• Low level input signal: x 0
• Fundamental component
• Same results as from small signal (linear) analysis
I0(x) = 1 o C m i
1m
T 0
v (t) R G (x)v (t)
I (x)IG (x) 2x V I (x)
-
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Gain change
• As signal amplitude increases, the gain decreases:compressionSmall signal
High compression
Output saturation: ≈ squarewave output high distortion:
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Signal level for 1 dB compression
• From Gm(x) curve:
Gm(x) = gm - 1 dB = 0,89 gm
x ≈ 1; Vi ≈ 26 mV
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Compressing amplifiers: where?
• RF signal have variable, unknown amplitude– In FM receivers, AM is noise compression OK– In AM receivers, AM is the useful signal NO compression
• FM IF amplifiers: remove AM (fast): – Compressing amplifiers
• AM IF amplifiers: keep AM, but …– Received signal amplitude changes (fading, slow)
– Need for AGC» Compensate slow changes» Ignore fast changes (modulation !)
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Gain compression: example
• Functional parameters:– Input level– Compression coefficient
• Circuit parameter– Resonant circuit Q
• Test B.3-a– Analysis of a compressing amplifier
» From input levels, compute AM index at the output
minVmaxVminVmaxV
m
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Gain stabilization: emitter feedback
• Input signal VI partitioned among VBE and RE
– Voltage drop on RE : RE iC– VBE = Vi – iC RE
VBE = Vi – Gm(x’) VBE RE
– x’ = VBE/VT ; x = Vi/VT
– x’ is defined by an equation without closed form solution:
• Can be solved only with successive approximation
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Gain with emitter feedback
-
i BET T
BE i C E C m BE
BE i m BE E
iBE
m E
m CO m C BE i
m E
m E
1
1
1
V Vx ; x'V VV V i R ; i G (x')V
V V G (x')V RVV
G (x')R
G (x')RV G (x')R V VG (x')R
xx'G (x')R
Can be solved only with successive approximation
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Frequency multipliers
• Input signal: sinewave at ωi
• Vi harmonics in the collectrocurrent IC
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Frequency multipliers
• Input signal at ωi
• Nonlinearity brings Vi harmonics in the IC (b)
• A tuned circuit isolates the planned harmonic (c)
– Different attenuationfor 2 ωi and 4 ωi
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Frequency multiplier: example
• Functional parameters (specs):– Multiplication factor N– Output spectral purity
• Circuit parameter (design)– Input amplitude– Tuned circuit Q
• Design problems– Design a frequency multiplier x N, from the input level and
spectral purity specifications– Compute the minimum Q required for the tuned circuit
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Frequency multiplier: test B.3-c
• Test B.3-c– An AM signal with Vmax = 260 mV; Vmin = 26 mV goes through
a BJT amplifier (without emitter feedback).– Find the modulation index Mo at the output
• Solution– x = 10 1– Gm/gm = 0,190 0,893 (slide B3-17)– Vo = - Rc Gm (x) Vi – M = (Vmax – Vmin)/(Vmax + Vmin);
» Input signal: Mi = 0,8 » Output signal:
Mo = (10 Gm (10) – Gm (1))/(10 Gm (10) + Gm (1)) = 0,36
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Lesson B3: final test
• Which are the techniques usable to reduce harmonic content and distortion in amplifiers?
• Is there any difference between the spectral content of collector current and of collector voltage in a tuned amplifier?
• Define large signal transconductance.
• Which parameters describe a RLC tuned circuit?
• Where can be useful a compressing amplifier?
• Describe how the Emitter DC voltage depends on input signal level.
• Define the 1-dB compression point.
• List the parameters which define the spectral purity of a frequency multiplier.