1. Common-Collector (Emitter-Follower) Amplifier

2. Remember that for Common Collector Amplifier,
the output is measured at the emitter terminal.
the gain is a positive value

3. β = 100
VBE = 0.7V
VA = 80 V

4. Perform DC analysis to obtain the value of IC
BE loop: 25IB IE – 2.5 = 0
25IB (1+ β)IB = 2.5
IC = βIB = mA
Calculate the small-signal parameters
r = 3.28 k , gm = 30.5 mA/V, ro = k

5. vb β = 100 VBE = 0.7 V VA = 80 V RS = 0.5 k 3.28 k gmvbe RTH = 25 kvS vO
3.28 k k vb
RE = 2 k
RS = 0.5 k
Output at emitter terminal
gmvbe

6. Redraw the small signal equivalent circuit so that all signal grounds connected together.x vS vi
RS = 0.5 k
RTH = 25 k
3.28 k x x vO
RE = 2 k x
gmvbe

7. RTH = 25 k vS vO
3.28 k k
RE = 2 k
RS = 0.5 k x
gmvbe vi

8. STEPS
OUTPUT SIDE
Get the equivalent resistance at the output side, Req
At node x, use KCL and get io in terms of vbe where io = gmvbe+ 𝑣𝑏𝑒 𝑟𝜋
Get the vo equation where vo = io Req
INPUT SIDE
Calculate Rib = r + (1+) Req
Calculate Ri = Rib // RTH
vbe in terms of vi using supermesh, vi = vbe + vo

9. Supermesh
Supermesh is defined as the combination of two meshes which have current source on their boundary

10. 2. At node x, use KCL and get io in terms of ib
RTH = 25 k vS vO
3.28 k k
RE = 2 k
RS = 0.5 k x
gmvbe vi
1. Get the equivalent resistance at the output terminal, Req  Req = ro ||RE = 1.96 k
2. At node x, use KCL and get io in terms of ib
 io = gmvbe+ 𝑣𝑏𝑒 𝑟𝜋 = vbe
3. Get the vo equation where vo = io Req
 vo = io Req = vbe

11. - 4. Calculate Rib = r + (1+) Req Rib = 3.28+101 (1.96) = 201.24 k
RS = 0.5 k x io + vO - vi
RTH = 25 k vS Ro
gmvbe
4. Calculate Rib = r + (1+) Req
Rib = (1.96) = k
5. Calculate Ri  Ri = RTH // Rib = k
6. vbe in terms of vi using supermesh
vi = vbe + vo = vbe vbe
vi = vbe

12. 5. Av vi = vo  open circuit voltage
Av vi = vbe = vi =
Av =  open circuit voltage gain
61.38

13. To find new voltage gain, vo/vs with input signal voltage source, vs
RS = 0.5 kΩ vS vo
Ri = 22.24 k
To find new voltage gain, vo/vs with input signal voltage source, vs
6. vi in terms of vs  use voltage divider:
vi = [ Ri / ( Ri + Rs )] * vs = vs
7. vo = Avvi  because there is no load resistor
vo = (0.978 vs)
vo/vs = 0.962

14. The voltage gain of common collector is less than 1.
Hence, the common collector doesn’t do any voltage amplification.
For that reason, this circuit is sometimes called a voltage follower.
But, as you can see, this circuit does have great potential as a current amplifier.

15. RTH = 15 k
VTH = V
The circuit above is a common collector configuration. Given  = 135 and VBEon = 0.66 V and VA = 
Calculate the DC collector current, IC
Draw the AC equivalent circuit

16. Perform DC analysis to obtain the value of IC
BE loop: 15IB IE – = 0
15IB (1+ β)IB = 1.594
15IB + 1(136)IB = IB = mA
IC = βIB = mA
Calculate the small-signal parameters
r = k , gm = mA/V, ro = 

17. 2. At node x, use KCL and get io in terms of ib
RTH = 15 k
4.19 k
RE = 1 k
gmvbe
r = k , gm = mA/V vi
1. Get the equivalent resistance at the output terminal, Req  Req = RE = 1 k
2. At node x, use KCL and get io in terms of ib
 io = gm𝑣𝑏𝑒 + 𝑣𝑏𝑒 𝑟𝜋 = 𝑣𝑏𝑒
3. Get the vo equation where vo = io Req
 vo = io Req = 𝑣𝑏𝑒

18. 4. Calculate Rib = r + (1+) Req Rib = 4.19 +136 (1) = 140.19 k
RTH = 15 k vi
gmvbe
RE = 1 k
r = k , gm = mA/V
4. Calculate Rib = r + (1+) Req
Rib = (1) = k
5. Calculate Ri  Ri = RTH // Rib = k
6. vbe in terms of vi using supermesh
vi = 𝑣𝑏𝑒 + vo = 𝑣𝑏𝑒 𝑣𝑏𝑒
vi = 𝑣𝑏𝑒

19. 5. Av vi = vo  open circuit voltage
Av vi = vbe = vi = 0.97
Av = 0.97  open circuit voltage gain
33.43

20. Now, we need to calculate RO
Ri = k v1
RL = 4 k
Now, we need to calculate RO
The calculation of RO for common-collector is based on using test voltage, Vx with current Ix

21. 𝑅𝑜= 𝑟𝜋 (1+𝛽) | 𝑅𝐸 |𝑟o + Vx - RTH 1. vbe in terms of vx vbe = - vx
the input voltage vi turned off + Vx -
RTH
1. vbe in terms of vx
𝑅𝑜= 𝑟𝜋 (1+𝛽) | 𝑅𝐸 |𝑟o
vbe = - vx
2. Use nodal analysis
Vx Vx Vx = gmvbe + Ix ro RE r
Vx Vx Vx =
- gm Vx + Ix

22. vo / v1 = 0.963 So back to our example, we can now calculate Ro
r = k , RE = 1 k, RTH = 15 k and ro = 
So, Ro = k
𝑅𝑜= 𝑟𝜋 (1+𝛽) | 𝑅𝐸 |𝑟o
Ro = k
Ri = k v1
RL = 4 k
vi in terms of vs
vi = v1  in parallel
vo = [ RL / ( RL + Ro )] * Avvi  this is because we have load resistor RL
vo = [ 4 / ( 4.030)] (0.97 v1)
vo / v1 = 0.963

23. CURRENT GAIN ii io Output side: io = vo / 4 = vo / 4
Ro = k ii
Ri = k
RL = 4 k v1 io
Output side: io = vo / 4 = vo / 4
Input side: ii = v1 / Ri = v1 / 13.55
Current gain
= io / ii
= vo (13.55) = *
= 3.262
v1 (4)

24. io
235 A ii
72 A
Current gain = io / ii = 235/72 = 3.26

25. AMPLIFIER
INPUT RESISTANCE, Ri
OUTPUT RESISTANCE, RO
Common Emitter
Equivalent to Ri as in the steps to find voltage gain
Equivalent to Ro as in the steps to find voltage gain
Common Collector
Use the formula or find Ro using test voltage, Vx with current Ix.

26. r = 1.12 k , gm = 156.54 mA/V, ro =  Given IC = 4.07 mA, = 175
VA =  vS vo
r = 1.12 k , gm = mA/V, ro = 

27. 2. At node x, use KCL and get io in terms of ib
RTH = 9 k
1.12 k
RE = 1 k
gmvbe
r = 1.12 k , gm = mA/V vi
1. Get the equivalent resistance at the output terminal, Req  Req = RE = 1 k
2. At node x, use KCL and get io in terms of ib
 io = gmvbe+ 𝑣𝑏𝑒 𝑟𝜋 = vbe
3. Get the vo equation where vo = io Req
 vo = io Req = vbe

28. 4. Calculate Rib = r + (1+) Req Rib = 1.12 +176 (1) = 177.12 k
RTH = 9 k
1.12 k
RE = 1 k
gmvbe
r = 1.12 k , gm = mA/V vi
4. Calculate Rib = r + (1+) Req
Rib = (1) = k
5. Calculate Ri  Ri = RTH // Rib = k
6. vbe in terms of vi using supermesh
vi = vbe + vo = vbe vbe
vi = vbe

29. vo = vbe
vi = vbe
Av vi = vo  open circuit voltage
Av vi = vbe = vi =
Av =  open circuit voltage gain
158.43

30. vo / vS = 0.9875 Since we have RL we have to calculate Ro
r = 1.12 k , RE = 1 k, RTH = 9 k and ro = 
So, Ro = k
𝑅𝑜= 𝑟𝜋 (1+𝛽) | 𝑅𝐸 |𝑟o
Ro = k
Ri = k
RL = 1 k vS
vi in terms of vs
vi = vS  in parallel
vo = [ RL / ( RL + Ro )] * Avvi  this is because we have load resistor RL
vo = [ 1 / ( )] ( vS)
vo / vS =

31. CURRENT GAIN ii io Output side: io = vo / 1 = vo / 1
Ro = k ii
Ri = k
RL = 1 k vs io
Output side: io = vo / 1 = vo / 1
Input side: ii = vS / Ri = vS / 8.565
Current gain
= io / ii
= vo (8.565) = * 8.565
= 8.46
vS (1)

32. 0.95 mA
0.11 mA