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 jschutt@emlab.uiuc.edu

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

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

MOSFET High-Frequency Model

CS - Three Frequency Bands

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)

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

CS - High-Frequency Response

CS - High-Frequency Response

CS - High-Frequency Response

CS – Miller Effect Define Ceq such that

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

CS – Miller Effect

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

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

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)

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

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

High-Frequency Hybrid-p Model

CE - Three Frequency Bands

CS – Miller Effect – Exact Analysis

CS – Miller Effect – Exact Analysis

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

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

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

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