Chapter 9 Frequency Response PART C: High Frequency Response
Discrete Common Source (CS) Amplifier Goal: find high cut-off frequency, f H 2 f H is dependent on internal capacitances V o Load Resistance will affect f H
9.5. High Frequency Model of CS Amplifier 3 Goal: find high cut-off frequency, f H
Miller Effect or Miller Multiplier K Impedance Z can be replaced with two impedances: Z connected between node and ground = Z/(-K) Z 2 connected between node 2 and ground = Z/(-/K) 4
Miller Effect or Miller Multiplier K High-frequency model 5 R sig =R sig R G input resistance V o R L = r o R D R L output resistance V o Miller Effect C = C gd (-K), C 2 = C gd (-/K) K =small signal gain= V 0 /V gs =+g m R L ; R L =r o R D R L
Estimating f H f H : First Estimate (Miller s Approximation) 6 A M f H = 2πC in R sig Miller Effect R sig = R sig R G C in = C gs + C C = C gd + g m R L Mid-band Gain R L = r o R D RL A M = R G R G + Rs ig g m R L
Ex9.8 7 Compare A M and f H with the ones found in example 9.3
9.5.2 Analysis Using Miller s Theorem 8 High-frequency model with Load Capacitance C L What is Load Capacitance?
Estimating f H f H : Second Estimate (Miller s Theorem) 9 A M f H = fp in 2 + fp out 2 /2 fp in = 2πC in R sig R sig = R sig R G C in = C gs + C gd + g m R L fp out = 2πC L R L R L = r o R D R L C L = C L + Cgd + /(g m R L ) C C 2
Example 9.5 0 Transfer function First approximation Second approximation Exact Value -3 db frequency = 9537 rad/s
Estimating f H f H : Third Estimate (Open Circuit Time Constants) A M
P9.60, P9.6: CS Amp 2 Omit the % contribution. Just calculate f H
Discrete Common Emitter (CE) Amplifier 3 Goal: find high cut-off frequency, f H f H is dependent on internal capacitances V o Load Resistance will affect f H
High Frequency Model of CE Amplifier 4 Goal: find high cut-off frequency, f H
Miller Effect or Miller Multiplier K High-frequency model 5 R sig =R sig R G input resistance R L = r o R C R L output resistance V o C C 2
Estimating f H 6 f H : First Estimate (Miller s Approximation) A M f H = 2πCinR sig Mid-band Gain A M = R B R B + Rsig r π R B Rsig + rx + r π g m R L R sig = r π [ r x + (RB R sig ] C in = C π + C C = C μ + gmr L Miller Effect
Ex9.0 7 Note the trade-off between gain and bandwidth
9.5.2 Analysis Using Miller s Theorem 8 High-frequency model with Load Capacitance C L Vo What is Load Capacitance? C
Estimating f H f H : Second Estimate (Miller s Theorem) 9 A M f H = fp in 2 + fp out 2 /2 fp in = 2πCinR sig fp out = R sig = r π [ r x + (RB R sig ] C in = C π + C μ + gmr L 2πCL R L R L = r o R C RL C L = CL + C μ + /(g m R L ) C C 2
Estimating f H 20 f H : Third Estimate (Open Circuit Time Constants) A M
P9.64, 9.65: CE Amp 2 Omit the % contribution. Just calculate f H
Summary 22 Low Frequency Response: The coupling and bypass capacitors cause the amplifier gain to fall off at low frequencies The low cut-off frequency can be estimated by considering each of these capacitors separately High Frequency Model: Both MOSFET and the BJT have internal capacitive effects that can be modeled by augmenting the device hybrid-π model with capacitances. Transition Frequency indicates the speed of the transistor MOSFET: f T = g m /2π(C gs +C gd ) BJT: f T = g m /2π(C π +C μ )
A figure-of-merit for the amplifier is the gain-bandwidth product (GB = A M f H ): tradeoff between gain and bandwidth while keeping GB High Frequency Response: Summary The internal capacitances of the MOSFET and the BJT cause the amplifier gain to fall off at high frequencies. An estimate of the amplifier bandwidth is provided by the frequency f H at which the gain drops 3dB below its value at midband (A M ). The high-frequency response of the CS and CE amplifiers is severely limited by the Miller effect Three methods: ) Miller s Approximation, 2) Miller s Theorem, 3) Open-circuit Time Constants 23