1. Solid-State Devices & Circuits
ECE 442
Solid-State Devices & Circuits
12. Frequency Response of
CS Amplifiers
Jose E. Schutt-Aine
Electrical & Computer Engineering
University of Illinois

2. MOSFET - Gate Capacitance Effect
Triode region:
Saturation region:
Cutoff:

3. MOSFET – Junction Capacitances
Overlap capacitance (gate-to-source):

4. MOSFET High-Frequency Model

5. CS - Three Frequency Bands

6. Unity-Gain Frequency fT
fT is defined as the frequency at which the short-circuit current gain of the common source configuration becomes unity
Define:
(neglect sCgdVgs since Cgd is small)

7. Calculating fT For s=jw, magnitude of current gain becomes unity at
fT ~ 100 MHz for 5-mm CMOS, fT ~ several GHz for 0.13mm CMOS

8. CS - High-Frequency Response

9. CS - High-Frequency Response

10. CS - High-Frequency Response

11. CS – Miller Effect
Define Ceq such that

12. CS – Miller Effect
fo is the corner frequency of the STC circuit

13. CS – Miller Effect

14. Example
Rsig = 100 kW, RG=4.7 MW, RD =15 kW, gm=1mA/V, rds=150 kW, RL=10 kW, Cgs=1 pF and Cgd=0.4 pF

15. Example (cont’)
Upper 3 dB frequency is at:

16. BJT Capacitances Base: Diffusion Capacitance: Cde (small signal)
where Qn is minority carrier charge in base
where tF is the forward transit time (time spent crossing base)

17. BJT Capacitances Base-emitter junction capacitance:
Cjeo is Cje at 0 V. Voe is EBJ built in voltage ~ 0.9 V

18. BJT Capacitances In hybrid pi model, Cde+Cje=Cp
Collector-base junction capacitance
Cmo is Cm at 0 V. Voc is CBJ built in voltage ~ 0.9 V
Cp is around a few tens of pF
Cm is around a few pF

19. High-Frequency Hybrid-p Model

20. CE - Three Frequency Bands

21. CS – Miller Effect – Exact Analysis

22. CS – Miller Effect – Exact Analysis

23. CS – Miller Effect – Exact Analysis
We neglect the terms in s2 since
Miller
If we multiply through by

24. CS – Miller Effect – Exact Analysis
From which we extract the 3-dB frequency point

25. CS – Miller Effect – Exact Analysis
If Gg is negligible
If Ri =0

26. Example
For the discrete common-source MOSFET amplifier shown, the transistor has VT = 1V, mCox(W/L) = 0.25 mA/V2, l = 0, Cgs = 3 pF, Cgd = 2.7 pF and VA = 20 V. Assume that the coupling capacitors are short circuits at midband and high frequencies.
Find the 3dB bandwidth if Ri=0
(b) Find the 3dB bandwidth if Ri= 10 kW