Chapter 9 Frequency Response. PART C: High Frequency Response


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1 Chapter 9 Frequency Response PART C: High Frequency Response
2 Discrete Common Source (CS) Amplifier Goal: find high cutoff frequency, f H 2 f H is dependent on internal capacitances V o Load Resistance will affect f H
3 9.5. High Frequency Model of CS Amplifier 3 Goal: find high cutoff frequency, f H
4 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
5 Miller Effect or Miller Multiplier K Highfrequency 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
6 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 Midband Gain R L = r o R D RL A M = R G R G + Rs ig g m R L
7 Ex9.8 7 Compare A M and f H with the ones found in example 9.3
8 9.5.2 Analysis Using Miller s Theorem 8 Highfrequency model with Load Capacitance C L What is Load Capacitance?
9 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
10 Example Transfer function First approximation Second approximation Exact Value 3 db frequency = 9537 rad/s
11 Estimating f H f H : Third Estimate (Open Circuit Time Constants) A M
12 P9.60, P9.6: CS Amp 2 Omit the % contribution. Just calculate f H
13 Discrete Common Emitter (CE) Amplifier 3 Goal: find high cutoff frequency, f H f H is dependent on internal capacitances V o Load Resistance will affect f H
14 High Frequency Model of CE Amplifier 4 Goal: find high cutoff frequency, f H
15 Miller Effect or Miller Multiplier K Highfrequency 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
16 Estimating f H 6 f H : First Estimate (Miller s Approximation) A M f H = 2πCinR sig Midband 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
17 Ex9.0 7 Note the tradeoff between gain and bandwidth
18 9.5.2 Analysis Using Miller s Theorem 8 Highfrequency model with Load Capacitance C L Vo What is Load Capacitance? C
19 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
20 Estimating f H 20 f H : Third Estimate (Open Circuit Time Constants) A M
21 P9.64, 9.65: CE Amp 2 Omit the % contribution. Just calculate f H
22 Summary 22 Low Frequency Response: The coupling and bypass capacitors cause the amplifier gain to fall off at low frequencies The low cutoff 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 hybridπ 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 )
23 A figureofmerit for the amplifier is the gainbandwidth 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 highfrequency response of the CS and CE amplifiers is severely limited by the Miller effect Three methods: ) Miller s Approximation, 2) Miller s Theorem, 3) Opencircuit Time Constants 23
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