1. Lecture 7
Frequency Response

2. Review of CS, CG and CD Amplifier

3. Voltage Gain of a CS Amplifier
Interpretation: The resistance at the drain
Divided by the resistance in the source path

4. Voltage Gain of a CD Amplifier

5. Voltage Gain of a CG Amplifier
If RS=0 and channel length modulation is ignored, Av is

6. Resistance into the Drain Terminal

7. Resistance into the Source Terminal

8. Miller Effect

9. Miller’s Theorem

10. Typical Application of Miller’s Theorem
Miller’s theorem is useful when Z appears in parallel with the main signal (i.e. the amplifier)

11. Limitation of Miller’s Theorem
Limitations:
Interaction of poles through R3 and C3.

12. Association of Poles with Nodes
Each pole is determined by the product of
Total capacitance seen from each node to ground
Total resistance seen at the node to ground
“Each node in the circuit contributes one pole to the transfer function”

13. Common-Gate Example

14. CS Stage Output Impedance Input Impedance “Nodal Method”
Miller Approximation
“Zx” method
Equivalent Circuit Analysis
KCL
Dominant pole

15. High Frequency Model of CS Stage

16. CS Trade-Off L(um) W(um) GDS (uS) CDB (fF) CGD(fF) CGS(fF) 2 5.78
3.613
5.19
1.84
98.16
800n
2.56
3.79
0.915
0.803
17.3
180n
0.86
5.72
0.056
0.273
1.20
120n
0.64
9.55
0.029
0.201
0.55
For Same IOUT,
L↓→W↓→GDS↑(Ro↓) →CDS ↓
Specs:
AV=10
Vo,cm=0.6V
I(M1)=10 uA
gm=AV/RD
Gmoverid_1=16.67
Trade-offs in GDS and parasitic
capacitance.

17. CS Trade-Off AV I (uA) L(um) W(um) GDS (uS) CDB (fF) CGD(fF) CGS(fF)10 2
5.78
3.613
5.19
1.84
98.16 15
32.5
5.33
27.5
10.4
517.8 20
668.2
6.66
319.6
239.8
6,041.1
For Same IOUT,
L↓→W↓→GDS↑(Ro↓) →CDS ↓
Specs:
Vo,cm=0.6V
gm=AV/RD
Difficult to achieve high gain and
high speed at the same time!

18. Output Impedance
Only Valid if Rs is large!

19. Input Impedance High frequency approximation Exclude CGS
(First order model)

20. Input Impedance (KCL) High frequency approximation Exclude CGS
(In parallel with CGS)

21. “Nodal Method”(Miller Approximation)
It is important
to identify the
high impedance node!
Numerical example:
RS=50 Ohms
L=2.0 um
AV=15
fin=4.65 GHz
fout=69.9 MHz
16(10.40fF)
517.8 fF
CDB=27.51 fF, RD=60 KOhm

22. Transfer Function

23. “Nodal Method”(Refined Miller Approximation)
(If RS is large!)
(Capacitive)
(Resistive)

24. Equivalent Circuit Analysis

25. Comparison to Miller Approximation

26. Dominant Pole Approximation

27. Transmission Zero Finding a transmission zero in effective Gm.

28. Source Follower
(Strong interaction between XY, making it difficult to associate
each pole with each node)

29. Source Follower

30. Transmission Zero
𝜔𝑧=−𝑔𝑚/(𝐶𝑔𝑠+𝐶𝑔𝑑)

31. Input Impedance

32. Analysis of Input Impedance
Miller Approximation:
Av:
(Negative Resistance)
Can be used to oscillators.

33. Output Impedance

34. Equivalent Output Impedance

35. Issues

36. Common Gate

37. Cascode
(Gain from A to X)

38. DC Input Resistance
Will a large Rin increase the miller effect of CS dramatically?

39. Input Resistance of Common Gate
Note that ZL is not infinity if RD is replaced by a current source because ZL is in parallel with CD.

40. Differential Pair (Differential Mode)
(Differential Half Circuit)

41. Differential Pair (Common-Mode)
W3 is made as large
as possible to minimize VDSAT.

42. Consequence of Limited CMRR

43. Differential Pair with High Impedance Load
AC Ground
(Dominant Pole)

44. Differential Pair Example
GM= uS
GDS= uS
RD=90 Kohm

45. AC analysis

46. Use the Waveform Calculator
Add voltages to the calculator
Press Eval before you plot

47. Plot in Magnitude/dB

48. Transfer Function
3dB Bandwidth: MHz

49. Differential Pair with Current Mirror

50. Small Signal Equivalent Model
(Transmission Zero)

51. Differential Pair with Current Mirror
(Slow Path)
(Fast Path)