CE/CS Amplifier Response at High Frequencies

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1 .. CE/CS Amplifier Response at High Frequencies INEL Manuel Toledo August 20, 2012 INEL Manuel Toledo CE/CS High Frequency Analysis 1/ 24

2 Outline.1 High Frequency Models.2 Simplified Method.3 Common-emitter.4 Miller Theorem.5 Unity Gain Frequency INEL Manuel Toledo CE/CS High Frequency Analysis 2/ 24

3 High Frequency Models G C gd r d D S C gs g m v gs S B C µ C r π v π C π g m v π r O E E small-signal incremental model PARASITIC CAPS LIMIT GAIN AT HIGH FREQS. INEL Manuel Toledo CE/CS High Frequency Analysis 3/ 24

4 CE High Frequency Model R TH B C µ C v S R B r π vπ C π g m v π R LL =R C R L R B =R 1 R 2 E INEL Manuel Toledo CE/CS High Frequency Analysis 4/ 24

5 Open-circuit time constant method.1 Replace all coupling and bypass caps by shorts.2 Select one parasitic cap; call it C H1.3 Replace all other parasitic caps by open circuits.4 Find resistance seen by C H1 ; call it R H1.5 High frequency pole associated with C H1 is 1 ω H1 = C H1 R H1.6 Repeat above steps for each parasitic cap.7 Find equivalent high frequency cutoff ω H = 1 n i=1 1 ω Hi INEL Manuel Toledo CE/CS High Frequency Analysis 5/ 24

6 Single-stage amplifier V CC R 1 R C C C2 R TH C C1 v S R 2 R E C E R L INEL Manuel Toledo CE/CS High Frequency Analysis 6/ 24

7 Single-stage amplifier R TH B C µ C v S R B r π vπ C π g m v π R LL =R C R L R B =R 1 R 2 E INEL Manuel Toledo CE/CS High Frequency Analysis 7/ 24

8 Resistance Seen by C π : Seen by C µ : R π = r π R B R TH i test R B R TH r π v π v test R µ g m v π R LL =R C R L INEL Manuel Toledo CE/CS High Frequency Analysis 8/ 24

9 R µ Resistance seen by C µ i test R B R TH r π v π v test R µ g m v π R LL =R C R L v π = i test (R B R TH r π ) INEL Manuel Toledo CE/CS High Frequency Analysis 9/ 24

10 R µ Applying KVL on the external loop yields v test = v π + (i test + g m v π )R LL = i test (R B R TH r π ) +(1 + g m (R B R TH r π ))i test R LL R µ = v test i test = R B R TH r π + R LL +g m (R B R TH r π )R LL INEL Manuel Toledo CE/CS High Frequency Analysis 10/ 24

11 Miller Theorem Y=sC i IN i OUT v in A m v out Assume that A m = v OUT v IN Use is negative and is independent of Y = sc. v OUT = A m v IN v IN = v OUT /A m INEL Manuel Toledo CE/CS High Frequency Analysis 11/ 24

12 Miller Theorem Input: i IN = Y (v IN v OUT ) = sc(1 A m )v IN = sc IN v IN i.e. from the input C looks like a bigger capacitor C(1 A m ). Output: i OUT = Y (v OUT v IN ) = sc(1 1 A m )v OUT = sc OUT v OUT i.e. from the output C looks like a capacitor C(1 1 A m ) C. INEL Manuel Toledo CE/CS High Frequency Analysis 12/ 24

13 Miller Theorem v IN C IN A m v OUT C OUT INEL Manuel Toledo CE/CS High Frequency Analysis 13/ 24

14 Miller Theorem To apply Miller s Theorem, make sure that A m is negative A m is real, i.e. load is resistive INEL Manuel Toledo CE/CS High Frequency Analysis 14/ 24

15 Unity-gain frequency: f t f t : frequency at which the transistor s β = 1. i c C µ i b i b Z b r π vπ C π g m v π i c INEL Manuel Toledo CE/CS High Frequency Analysis 15/ 24

16 Unity-gain frequency: f t i c = g m v π v π sc µ Z b = r π = = v π = i b Z b 1 1 sc π 1 1 sc µ r π + sc π + sc µ r π 1 + sr π (C π + C µ ) INEL Manuel Toledo CE/CS High Frequency Analysis 16/ 24

17 Unity-gain frequency: f t Midband β β 0 = g m r π β has a pole at β(s) = i c = ω β = i b g m r π sr π C µ 1 + sr π (C π + C µ ) β sr π (C π + C µ ) 1 r π (C π + C µ ) INEL Manuel Toledo CE/CS High Frequency Analysis 17/ 24

18 Unity-gain frequency: f t f t : f at which β(s) = 1 β 2 0 = 1 + ω2 t ω 2 β ω t = ω β β β 0ω β Data sheet often specifies f t and C µ ; C π can then be found from above equations. INEL Manuel Toledo CE/CS High Frequency Analysis 18/ 24

19 Example A common-source amplifier is constructed with a 10µF bypass capacitor in parallel with a 1kΩ resistor, both connected to the FET s source terminal. The equivalent resistance seen by the bypass capacitor is 100Ω. At high frequencies there is a single pole located at 1MHz. If the amplifier s midband gain is 80dB, find an expression for the amplifer s gain as a function of the complex frequency s, valid for low-, mid- and high-frequencies. INEL Manuel Toledo CE/CS High Frequency Analysis 19/ 24

20 A common-source amplifier is constructed with a 10µF bypass capacitor in parallel with a 1kΩ resistor, both connected to the FET s source terminal. The equivalent resistance seen by the bypass capacitor is 100Ω. At high frequencies there is a single pole located at 1MHz. If the amplifier s midband gain is 80dB, find an expression for the amplifer s gain as a function of the complex frequency s, valid for low-, mid- and high-frequencies. ANSWER: A v (s) = 10 4 s s s 2π INEL Manuel Toledo CE/CS High Frequency Analysis 20/ 24

21 Example For the circuit shown below, find (i) the pole frequency applying Miller s theorem; (ii) the pole frequency using the open-circuit time constant method; and (iii) an expression for the voltage gain A v (s) = v OUT v S as a function of complex frequency s, valid for midand high-frequencies. 10k C 1 =10-11 F 1k v S 5k - v v 1 1k + v OUT - INEL Manuel Toledo CE/CS High Frequency Analysis 21/ 24

22 Example For the circuit shown below, find (i) the pole frequency applying Miller s theorem; (ii) the pole frequency using the open-circuit time constant method; and (iii) an expression for the voltage gain A v (s) = v OUT v S as a function of complex frequency s, valid for midand high-frequencies. 10k C 1 =10-11 F 1k v S 5k - v v 1 1k + v OUT - ANSWER: (i) 297krps; (ii) 297krps (iii) A v (s) = s 297krps +1 INEL Manuel Toledo CE/CS High Frequency Analysis 22/ 24

23 Prob A CS amplifier is specified to have g m = 5mA/V, r o = 40kΩ, C gs = 2pF, C gd = 0.1pF, C L = 1pF, R sig = 20kΩ, and R L = 40kΩ. (a) Find the low-frequency gain A M and use open-circuit time constants to estimate the 3-dB frequency f H. Hence determine the gain-bandwidth product. (b) If a 500Ω resistance is connected in the source lead, find the new values of A M, f H, and the gain-bandwidth product. Assume g mb = 1mA/V. INEL Manuel Toledo CE/CS High Frequency Analysis 23/ 24

24 Prob INEL Manuel Toledo CE/CS High Frequency Analysis 24/ 24

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Quick Review. ESE319 Introduction to Microelectronics. and Q1 = Q2, what is the value of V O-dm. If R C1 = R C2. s.t. R C1. Let Q1 = Q2 and R C1 Quick Review If R C1 = R C2 and Q1 = Q2, what is the value of V O-dm? Let Q1 = Q2 and R C1 R C2 s.t. R C1 > R C2, express R C1 & R C2 in terms R C and ΔR C. If V O-dm is the differential output offset ECE 202 Fall 2013 Final Exam December 12, 2013 Circle your division: Division 0101: Furgason (8:30 am) Division 0201: Bermel (9:30 am) Name (Last, First) Purdue ID # There are 18 multiple choice problems We re going to look at emitter degeneration in detail today. The purpose is in part to review, and in part to help pull together a few of the concepts that we ve dealt with in the class up to this point.