Emitter-Follower (EF) Amplifier

1
Emitter-Follower (EF) Amplifier

• DC biasing
• Calculate IC, IB, VCE
• Determine related small signal equivalent
  circuit parameters
• Transconductance gm
• Input resistance rp
• Midband gain analysis
• Low frequency analysis
• Gray-Searle (Short Circuit) Technique
• Determine pole frequencies ?PL1, ?PL2, ...
  ?PLn
• Determine zero frequencies ?ZL1, ?ZL2,
  ... ?ZLn
• High frequency analysis
• Gray-Searle (Open Circuit) Technique
• Determine pole frequencies
• ?PH1, ?PH2, ... ?PHn
• Determine zero frequencies ?ZH1, ?ZH2,
  ... ?ZHn

High and Low Frequency AC Equivalent Circuit
2
EF Amplifier - DC Analysis (Nearly the Same
as CE Amplifier)

• GIVEN Transistor parameters
• Current gain ß 200
• Base resistance rx 65 O
• Base-emitter voltage VBE,active 0.7 V
• Resistors R110K, R22.5K, RC1.2K, RE0.33K
• Form Thevenin equivalent for base given VCC
  12.5V
• RTh RB R1R2 10K2.5K 2K
• VTh VBB VCC R2 / R1R2 2.5V
• KVL base loop
• IB VTh-VBE,active / RTh(ß 1)RE
• IB 26 µA
• DC collector current IC ß IB
  
  IC 200(26 µ A) 5.27 mA
• Transconductance gm IC / VT VT kBT/q
  26 mV gm 5.27 mA/26 mV 206 mA/V
• Input resistance rp ß / gm 200/206
  mA/V 0.97 K
• Check on transistor region of operation
• KVL collector loop
• VCE VCC - (ß 1) IB RE 10.8 V (was 4.4 V
  for CE amplifier) (okay since not close to zero
  volts).

R1 10K R2 2.5K RC 0 K RE 0.33K
Note Only difference here from CE case is
VCE is larger since RC was left out here
in EF amplifier.
3
EF Amplifier - Midband Gain Analysis
DC analysis is nearly the same! IB , IC and gm
are all the same. Only VCE is different since
RC0.
Ip


Ri
Vb
Vi
VO
_
_
Equivalent input resistance Ri
NOTE Voltage gain is only 1! This is a
characteristic of the EF amplifier! Cannot get
voltage gain gt1 for this amplifier!
4
Analysis of Low Frequency Poles Gray-Searle
(Short Circuit) Technique

• Draw low frequency AC circuit
• Substitute AC equivalent circuit for transistor
  (hybrid-pi for bipolar transistor)
• Include coupling capacitors CC1, CC2
• Ignore (remove) all transistor capacitances Cp ,
  Cµ
• Turn off signal source, i.e. set Vs 0
• Keep source resistance RS in circuit (do not
  remove)
• Consider the circuit one capacitor Cx at a time
• Replace all other capacitors with short circuits
• Solve remaining circuit for equivalent resistance
  Rx seen by the selected capacitor
• Calculate pole frequency using
• Repeat process for each capacitor finding
  equivalent resistance seen and corresponding pole
  frequency
• Calculate the final low 3 dB frequency using

5
Emitter Follower - Analysis of Low Frequency
Poles Gray-Searle (Short Circuit) Technique
Input coupling capacitor CC1 2 µF
IX
Ip
Ri
Vi
6
Emitter Follower - Analysis of Low Frequency
Poles Gray-Searle (Short Circuit) Technique

• Output coupling capacitor CC2 3 µF

Ip
Ve

• Low 3 dB frequency

Ie
re
IX
So dominant low frequency pole is due to CC1 !
7
Emitter Follower - Low Frequency Zeros

• What are the zeros for the EF amplifier?
• For CC1 and CC2 , we get zeros at ? 0 since
  ZC 1 / ?C and these capacitors are in the
  signal line, i.e. ZC ? ? at ? 0 so Vo ? 0.

8
Emitter Follower - Low Frequency Poles and
ZerosMagnitude Bode Plot
9
Emitter Follower - Low Frequency Poles and
ZerosPhase Shift Bode Plot
10
Analysis of High Frequency Poles Gray-Searle
(Open Circuit) Technique

• Draw high frequency AC equivalent circuit
• Substitute AC equivalent circuit for transistor
  (hybrid-pi model for transistor with Cp, Cµ)
• Consider coupling and emitter bypass capacitors
  CC1 and CC2 as shorts
• Turn off signal source, i.e. set Vs 0
• Keep source resistance RS in circuit
• Neglect transistors output resistance ro
• Consider the circuit one capacitor Cx at a time
• Replace all other transistor capacitors with open
  circuits
• Solve remaining circuit for equivalent resistance
  Rx seen by the selected capacitor
• Calculate pole frequency using
• Repeat process for each capacitor
• Calculate the final high frequency pole using

11
Emitter Follower - Analysis of High Frequency
Poles Gray-Searle (Open Circuit) Technique
Ie

• Redrawn High Frequency Equivalent Circuit

zp 1/yp
E
Ie
Zeq
12
Emitter Follower - Analysis of High Frequency
Poles Gray-Searle (Open Circuit) Technique
ZB
zp 1/yp
Replace this with this.
Modified Equivalent Circuit
ZB
Looks like a resistor in parallel with a
capacitor.
13
Emitter Follower - Analysis of High Frequency
Poles Gray-Searle (Open Circuit) Technique
RxCp

• Pole frequency for Cp 17 pF

14
Emitter Follower - Analysis of High Frequency
Poles Gray-Searle (Open Circuit) Technique

• Pole frequency for Cµ 1.3 pF

15
Emitter Follower - Analysis of High Frequency
Poles Gray-Searle (Open Circuit) Technique

• Alternative Analysis for Pole Due to Cp

Ix-Ip
Ix
Vx
Ip
E
Ie
IegmVp
We get the same result here for the high
frequency pole associated with Cp as we did
using the equivalent circuit transformation.
16
Emitter Follower - Analysis of High Frequency
Poles Gray-Searle (Open Circuit) Technique

• Alternative Analysis for Pole Due to Cµ

Ix-Ip
Ix
Vx
Ip
E
IpgmVp
We get the same result here for the high
frequency pole associated with Cµ as we did
using the equivalent circuit transformation.
17
Emitter Follower - High Frequency Zeros

• What are the high frequency zeros for the
  EF amplifier?
• Voltage gain can be written as
• When Vo/Vp 0, we have found a zero.
• For Cµ , we get Vo ? 0 when ? ? ? since
  the node B will be shorted to ground and
  Vp 0 .
• Similarly, we get a zero from Cp when
  yp gm 0 since we showed earlier that
• Also, can see this from

18
Emitter Follower - High Frequency Poles and
ZerosMagnitude
19
Emitter Follower - High Frequency Poles and
ZerosPhase Shift
20
Comparison of EF to CE Amplifier (For RS
5O )
CE EF
Midband Gain Low Frequency Poles and
Zeros High Frequency Poles and Zeroes
Better low frequency response !
Much better high frequency response !
21
Conclusions

• Voltage gain
• Can get good voltage gain from CE but NOT from EF
  amplifier (AV ? 1).
• Low frequency performance better for EF
  amplifier.
• EF amplifier gives much better high frequency
  performance!
• CE amplifier has dominant pole at 5.0x107 rad/s.
• EF amplifier has dominant pole at 1.0x1010 rad/s.
• Bandwidth approximately 200 X larger!
• Miller Effect multiplication of C? by the gain is
  avoided in EF.
• Current gain
• For CE amplifier, current gain is high ? Ic/Ib
• For EF amplifier, current gain is also high
  Ie/Ib ? 1 !
• Frequency dependence of current gain similar to
  voltage gain.
• Input and output impedances are different for the
  two amplifiers!