1

Conventional amplifier

Collector

Emitter

Base

Rb1

Rb2

Rc

Re Ce

RL

Vcc

Vin

Vout

Av = Vout/Vin = - (Rc//RL) / re

re = ac resistance of the emitter

2

High-frequency transformer-coupled amplifier

Collector

Emitter

Base

Rb1

Rb2

RL

ReCe

Vcc

C1

Vin

Vout

f = 1 / (2 pi sqrt(L C1)

Q = f / B

L

Example 2.1

3

Practical common emitter amplifier with better impedance matching

Collector

Emitter

Base

Rb1

Rb2

RL

ReCe

Vcc

C1

Vin

VoutL

Rd

Cd

Better impedance matching

Higher Q

4

Common base RF amplifier

RL

ReCb

Vin

VoutL L

Vcc

5

Wideband amplifier- Class A

Collector

Emitter

Base

Rb1

Rb2

RL

ReCe

Vcc

Vin

Vout

L

Linear amplifier

Generally used as single-ended audio amplifiers

6

Wideband amplifier- Class B

Rb1

RL

Vcc

Vin

Vout

Compared to Class A:

Greater efficiency

Larger distortion

7

Amplifier- Class C

Collector

Emitter

Base

RL

Vcc

Vin

Vout

L

High efficiency

Larger distortion

8

Operating condition

Class C amplifiers would improve the efficiency by operating in nonlinear regime, however the input has to be a sinusoidal wave

Some means are needed to remove the distortion and restore the signal to its original sine shape

9

Operation principle

The active device conducts for less than 180 degrees of the input cycle

The output resembles a series of pulses more than it does the original signal

The pulses can be converted back to sine waves by an output tuned circuit

10

Circuit configuration

Collector

Emitter

Base

RL

Vcc

Vin

Vout

L

Input

Output

Nonlinear amplifier

Sine input -> nonlinear current output -> sine output

Fig. 2.12

11

Pros and Cons of the Class C amplifiers

Pros:

• High efficiency, no current in absence of signal

Cons:

• The output tuned circuit must be adjusted fairly close to the operating frequency

• The amplification is nonlinear

12

Comparison of three amplifiers

Class A B C

Conduction angle

360 180 < 180

Maximum efficiency

50% 78.5% 100%

Likely practical efficiency

25% 60% 75%

13

Neutralization

Collector

Emitter

Base

Rb1

Rb2

RL

ReCe

Vcc

Vin

VoutL

Rd

Cd

Cn Neutralization capacitor

14

Oscillator

A

B

Barkhausen criteria:

• A x B = 1

• Phase shift must total 0 or integer multiple of 360 degrees

15

Using non-inverting amplifier

Hartley oscillator

B = N1 / (N1 + N2)

f = 1/2pi sqrt(LC)

N2

N1

16

Using inverting amplifier (Hartley oscillator)

B = -N1 / N2 B = (N1 + N2) / N1

Example 2.2

N2

N1

N2

N1

17

Colpitts oscillator (non-inverting amplifier)

B = Xc1 / Xct = C2 / (C1 + C2)

C2

C1

18

Colpitts oscillator (inverting amplifier)

Example 2.3

B = -Xc1/Xc2 = - C2/C1

C2

C1

19

Clapp oscillator

20

Varactor tuned oscillator

Example 2.5

C=C0/sqrt(1+2V)

21

Oscillation frequency of LC circuit

See MIT open course ware

22

Another application of high Q filter

Before After

Clock recovery by strong filtering effect

PTL Oct

23

Crystal

Crystal oscillators achieve greater stability by using a small slab of quartz as a mechanical resonator, in place of an LC tuned circuit

Cs Cp

Two resonance frequency related to Cs and Cp, respectively

24

fT = f0 + k f0(T-T0)

Example 2.6

A portable radio transmitter has to operate at temperatures from –5 to 35 degrees. If the frequency is derived from a crystal oscillator with a temperature coefficient of +1ppm/degree C and it transmits at exactly 146 MHz at 20 degree, find the transmitting frequencies at the two extremes of the operating range

Temperature dependence

25

Mixers

A mixer is a nonlinear circuit that combines two signals in such a way as to produce the sum and difference of the two input frequencies at the output

Any nonlinear device can operate as a mixer

Vout = A Vi + B Vi2 + C Vi3 + …

f1 f2f1+f2f1- f2

Second order effects

26

Square law mixers

Vout = A Vi + B Vi2

If inputs are two frequencies,

the outputs will be:

Original frequencies, double frequencies, sum frequencies, and differential frequencies

Example 2.7

27

Diode mixers

The V-I curve for a typical silicon signal diode is nonlinear

Diode mixers can operate between reverse and forward biased states

Or they can operate with a small forward bias

28

Transistor mixers

Collector

Emitter

Base

Rb1

Rb2

RL

Re

Vcc

f1

Vout

L

f2

29

Balanced mixers

A multiplier circuit, where the output amplitude is proportional to the product of two input signals, can be used as a balanced mixer

V1 = sinω1t

V2 = sinω2t

Vo = V1 x V2 = 0.5 x [cos(ω1t - ω2t) – cos(ω1t + ω2t)]

30

Applications of balanced mixers

AM Modulation

Data (…01101001…)

Carrier

Output Signal

AM de-modulation

Signal input

Local oscillator

Output Signal

Filter

31

Detection schemes

Signal input

Output Signal

Filter

Self-mixing homodyne detection

Homodyne and heterodyne detection

One example of heterodyne detection

32

Phase detector using mixer

Signal input

The DC output depends on the phase of the two paths

33

Phase locked loop

Phase detector

LPF Amp VCO

OutputInput

Capture range

Lock range

Example 2.8

34

Simple frequency synthesizer

Phase detector

LPF Amp VCO

OutputInput

/ N divider

FM and AM channel spacing

Example 2.9

35

A practical example – 29M to 10G synchronization circuit

200

10

MAV11100

Clk ResetD1D0

74F163Counter

29MHzpulsein

5V

MAV11

D Q_

Clk Q74F74

D Flip-Flop

4.84 MTTL

Output

7K

4.7u150 150

4.7u

15V

MRV901

4K

1K

29MHz / 6 circuit

29MHz amplification, digitization and frequency division circuit (All capacitors are 0.1uF).

36

2K

10K

10K 100K

+6V 5

8

UPG506B 14GHz divide by 8 Prescalar

2.2V Zener

1000UF

10GHVCO

Splitter

+15V To 10G laser

1.5K

1.5K

+17V

10 dBm 2-10 dBm

1

UPB1502 1.25GHz divide by 128 Prescalar

2

3

4

8

7

6

5

-15~0 dBm

74F86 XOR gate

4.84 MHz TTL Input

74F74 f/2

5M to 10G synchronization circuit

37

Spectrum of 4.827MHz square signal wave. Span: 500Hz, RB: 30Hz. 

Spectrum of 4.827MHz square signal wave. Span: 500Hz, RB: 30Hz.

Experimental results

38

Pre-scaling

Phase detector

LPF Amp VCO

OutputInput

Fixed /M

Programmable /N

Fixed /Q

Example 2.10

39

Frequency translation

The movement of a block of frequencies is called a frequency translation

Two configurations:

Synthesizer with frequency shifting

Synthesizer with mixer in the loop

Example 2.11

40

Transmission lines

Coaxial cables (solid dielectric, air dielectric)

Parallel line cables (television twin-lead, open-wire line, shielded twin-lead)

Twisted pair cable

41

Two models of short transmission line section

Balanced line

Unbalanced line

42

Step and pulse response of lines

Characteristic impedance: the ratio of voltage to current through the transmission line with a step signal

Concept of matched line

Characteristic impedance Z0 = sqrt[(R + jwL) / (G + jwC)]

Many lines approach Z0 = sqrt(L/C)

Example 14.1, 14.2

43

Reflection (step input)

Open end scenario

Short end scenario

Pulse input…

44

Some definitions

Γ = Vr/Vi: reflection efficient

Γ = (ZL – Z0) / (ZL + Z0)

Meaning of the above equation:

1. To have zero reflection, ZL has to be equal to Z0

2. By measuring Γ, ZL can be derived to probe the internal characteristic of the load

Example 14.13

45

An example to know the internal parameters of a tunable laser

Lp

Cp

Rp

Cs

Rsub

D

Parasitics PN junction

Rs

SourceTransmission

line

S11

S11 = (ZL – Z0) / (ZL + Z0)

Parameters Reflector biased at 10 mA

Is (A) 1.79E10-5

q 4.47

Rp (ohm) 0.1

Rs (ohm) 0.1

Rsub (ohm) 1.0

Cp (pF) 4.58

Cs (pF) 355

Lp (nH) 21.4

46

Voltage driver is better than current driver

Current response Optical response

Y. Su et al, IEEE PTL Sept. 2004

47

Wave propagation

In a matched line, a sine wave moves down the line and disappear into the load. Such a signal is called a traveling wave

Example 14.5

RF Phase shifter

48

Standing waves

The interaction between the incident and reflected waves causes what appears to be a stationary pattern of waves on the line, which are called standing waves

SWR = Vmax/Vmin

For a matched line, the SWR = 1

49

Relation between Γ and SWR

SWR = (1+ |Γ|) / ( 1 - |Γ|)

If ZL >Z0,

SWR = Z0 / ZL

Example 14.6

50

51