ANALOGUE ELECTRONICS CIRCUITS I EKT 204 Frequency Response of FET Amplifiers 1

LOW-FREQUENCY AMPLIFIER RESPONSE  Input RC Circuit  Output RC Circuit  Bypass RC Circuit 2

FET Amplifier RLRL RSRS RDRD RGRG C1C1 C2C2 ViVi +V DD C3C3 R Si VoVo Common-source FET amplifier 3

Input RC circuit Output RC circuit Bypass RC circuit Low-frequency Equivalent Circuit 4

Input RC circuit The cutoff frequencies defined by the input, output and bypass circuits can be obtained by the following formulas: where R C1 =R Si +R G Input RC circuit 5

Output RC circuit where R C2 =R D +R L Output RC circuit 6

Bypass RC circuit where R C3 =R S ||1/g m Bypass RC circuit 7

Low cut-off frequency Hence, f C = the largest of the three low cut-off frequency 8

Example RLRL RSRS RDRD RGRG C1C1 C2C2 ViVi +V DD C3C3 R Si VoVo 1K  20V 10K  4.7K  2.2K  1M  0.5  F0.01  F 2F2F Determine the lower cutoff frequency for the FET amplifier. Given K = 0.4mA/V 2, V TN = 1V, = 0 9

Input RC circuit Output RC circuit Bypass RC circuit Solution 10

Since f c in bypass RC circuit is the largest of the three cutoff frequencies, it defines the low cutoff frequency for the amplifier:  f c = Hz 11

HIGH-FREQUENCY AMPLIFIER RESPONSE  Input RC Circuit  Output RC Circuit 12

HIGH-FREQUENCY Small capacitances exist between the gate and drain and between the gate and source. These affect the frequency characteristics of the circuit. roro C gd V gs g m V gs C gs - + hi-frequency hybrid-  model 13

Basic data sheet for the BS 107 n-MOSFET C gs = C iss - C rss C gd = C rss 14

Unity-Gain Bandwidth Unity gain frequency / bandwidth, f T 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

FET Amplifier In high-frequency analysis, coupling and bypass capacitors are assumed to have negligible reactances and are considered to be shorts. vovo RLRL RSRS RDRD R1R1 C1C1 C2C2 vivi +V DD C3C3 R Si R2R2 16

R 1 ||R 2 C Mo ViVi C gs R Si R D ||R L C Mi g m V gs VoVo R TH1 R TH2 High-frequency hybrid-  model with Miller effect A : midband gain 17

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: R TH1 C in vivi (a) Input circuit whereR TH1 = R Si ||R 1 ||R 2 and C in = C gs + C Mi R TH2 C out vivi (b) Output circuit where R TH2 = R D ||R L and C out = C Mo 18

Example Find the cutoff frequency of the input and output RC circuit for the FET amplifier in figure below. Given that C gd =0.1pF, C gs =1pF, K =0.5mA/V 2 and V TN =2V, =0. vovo RLRL RSRS RDRD R1R1 C1C1 C2C2 vivi +V DD C3C3 R Si R2R2 4 k  234 k  10 k  166 k  0.5 k  20 k  10 V 19

Solution DC Analysis 20

Input RC circuit Midband gain  Thevenin’s equivalent resistance at the input  total input capacitance  upper cutoff frequency introduced by input capacitance 21

Output RC circuit  total output capacitance  Thevenin’s equivalent resistance at the output  upper cutoff frequency introduced by output capacitance 22