ANALOGUE ELECTRONICS I EMT 112/4 Frequency Response of FET Amplifiers

LOW-FREQUENCY AMPLIFIER RESPONSE Input RC Circuit Output RC Circuit Bypass RC Circuit

FET Amplifier +VDD RD C2 RSi C1 Vo RL RG Vi C3 RS Common-source FET amplifier

Low-frequency Equivalent Circuit Input RC circuit Output RC circuit Bypass RC circuit

The cutoff frequencies defined by the input , output and bypass circuits can be obtained by the following formulas: Input RC circuit where RC1=RSi+RG Input RC circuit

Output RC circuit where RC2=RD+RL Output RC circuit

Bypass RC circuit where RC3=RS||1/gm Bypass RC circuit

Low cut-off frequency Hence, fC = the largest of the three low cut-off frequency

Example RL RS RD RG C1 C2 Vi +VDD C3 RSi Vo 1K 20V 10K 4.7K 2.2K 1M 0.5F 0.01F 2F Determine the lower cutoff frequency for the FET amplifier. Given K = 0.4mA/V2, VTN= 1V,  = 0

Solution Input RC circuit Bypass RC circuit Output RC circuit

Since fc in bypass RC circuit is the largest of the three cutoff frequencies, it defines the low cutoff frequency for the amplifier:  fc = 238.73Hz

HIGH-FREQUENCY AMPLIFIER RESPONSE Input RC Circuit Output RC Circuit

hi-frequency hybrid- model HIGH-FREQUENCY Small capacitances exist between the gate and drain and between the gate and source. These affect the frequency characteristics of the circuit. ro Cgd Vgs gmVgs Cgs - + hi-frequency hybrid- model

Basic data sheet for the BS 107 n-MOSFET Cgs = Ciss - Crss Cgd = Crss

Unity-Gain Bandwidth Unity gain frequency / bandwidth, fT is defined as a frequency at which the magnitude of the short-circuit current gain goes to 1 It is a parameter of FET & is independent of circuit Page 521

FET Amplifier In high-frequency analysis, coupling and bypass capacitors are assumed to have negligible reactances and are considered to be shorts. vo RL RS RD R1 C1 C2 vi +VDD C3 RSi R2

High-frequency hybrid- model with Miller effect RTH1 RTH2 RSi Vo R1||R2 Vi Cgs CMi CMo RD||RL gmVgs A : midband gain

The cutoff frequencies defined by the input and output circuits can be obtained by first finding the Thevenin equivalent circuits for each section as shown below: RTH2 RTH1 Cin Cout vi vi (a) Input circuit (b) Output circuit where RTH1 = RSi||R1||R2 and Cin = Cgs + CMi where RTH2 = RD||RL and Cout = CMo

Example Find the cutoff frequency of the input and output RC circuit for the FET amplifier in figure below. Given that Cgd=0.1pF, Cgs=1pF, K =0.5mA/V2 and VTN=2V, =0. vo RL RS RD R1 C1 C2 vi +VDD C3 RSi R2 4 k 234 k 10 k 166 k 0.5 k 20 k 10 V

Solution DC Analysis

Input RC circuit Midband gain  Thevenin’s equivalent resistance at the input  total input capacitance  upper cutoff frequency introduced by input capacitance

Output RC circuit  Thevenin’s equivalent resistance at the output  total output capacitance  upper cutoff frequency introduced by output capacitance