ECEN 326 Electronic Circuits

Transcription

1 ECEN 326 Electronic Circuits Frequency Response Dr. Aydın İlker Karşılayan Texas A&M University Department of Electrical and Computer Engineering

2 High-Frequency Model BJT & MOS B or G r x C f C or D r in v C in g m v g mb v 2 r o v 2 B E or S General BJT MOS r x r b 0 r in r π C in C π C gs C f C µ C gd r o r o r o g m g m g m g mb 0 g mb ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response

3 BJT & MOS Capacitances Active BJT: C π = C b + C je = τ F g m + C je C µ = C µo V ψ o n C π C µ MOS: C gs = 2 3 WLC ox C gd : Overlap capacitance C gs C gd ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 2

4 Transition Frequency, f T BJT & MOS i o i o i i i i r x C f i i r in v C g m v in r o io i o i i (s) g m r in + r in (C in + C f )s ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 3

5 Transition Frequency, f T BJT & MOS i o i i (jω) g m r in + r in (C in + C f )jω At high frequencies: i o i i (jω) g m (C in + C f )jω i o (jω) = i i ω=ω T g m (C in + C f )ω T = ω T = g m C in + C f, f T = ω T 2π BJT: ω T = g m C π + C µ MOS: ω T = g m C gs + C gd ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 4

6 BJT-CE & MOS-CS Small-signal circuit V o V o V i V i v i R S r x C f v o r in v C in g m v r o R L ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 5

7 BJT-CE & MOS-CS Transfer function v o v i (s) = K s C f g m + a s + a 2 s 2 K = g mr OL R + r x = g m R OL r in + r x + r in a = C f R OL + C f R + C in R + g m R OL RC f a 2 = R OL RC f C in R = ( + r x ) r in R OL = r o ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 6

8 BJT-CE & MOS-CS Poles & zeros D(s) = + a s + a 2 s 2 = s p s p 2 p 2 p p a, p 2 a a 2 p = R C in + C f + g m R OL + R OL R p 2 = g m R OL C f RC in R OL C in C in N(s) = s z z = g m C f ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 7

9 Miller Approximation Z x V i A V o Z i Z i = V i I i = V i V i V o Z x = V i V i ( AV i ) Z x = Z xv i (A + )V i = Z x A + Z x = sc Z i = s(a + )C = sc, C = (A + )C ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 8

10 Miller Capacitance +r x C f v i v o r in v C in v g m r o Miller Approximation v i +r x v o r in v C in C M v g m r o C M = (A + )C f, A = v o v = g m (r o ) ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 9

11 BJT-CE & MOS-CS Approximate solution v i +r x v o r in v C in +C M v g m R OL v o v i = g m R OL r in s(c in + C M ) + r x + r in s(c in + C M ) = g m R OL r in + r x + r in + s(c in + C M )R R = ( + r x ) r in, R OL = r o ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 0

12 Approximate vs. Exact Solution Miller approximation: Exact derivation: p = R(C in + C f ( + g m R OL )) p = R C in + C f + g m R OL + R OL R p 2 = g m R OL C f RC in R OL C in z = g m C f C in ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response

13 BJT-CE Poles & zeros p = (( + r b ) r π ) C π + C µ + g m R OL + R OL R p 2 = z = g m C µ g m R OL C µ RC π R OL C π C π ω T = g m C π + C µ p 2 p, p 2 > ω T, z > ω T ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 2

14 MOS-CS Poles & zeros p = p 2 = z = g m C gd C gs + C gd + g m R OL + R OL + + R OL C gd C gs R OL C gs + g m C gs ω T = g m C gs + C gd p 2 p, p 2 > ω T, z > ω T ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 3

15 BJT & MOS Differential Pair DM v id 2 v od 2 v id 2 v od 2 Dominant pole of v od v id (s) : p = R C in + C f + g m R OL + R OL R R = ( + r x ) r in, R OL = r o ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 4

16 BJT & MOS Differential Pair CM v ic v oc v ic v oc 2R T C T /2 2RT /2 C T A cm (s) Z T, Z T = 2R T sc T /2 = 2R T + sc T R T A cm (s) 2R T ( + sc T R T ) ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 5

17 BJT & MOS Differential Pair CMRR A cm db A dm db +20 db/dec ω log scale 20 db/dec ω R T C T CMRR db ω log scale ω 2 R(C in + C M ) ω ω 2 ω log scale ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 6

18 BJT-CC & MOS-CD Small-signal circuit V i V i V o V o v i r x r in v C in g m v r o g mb v o ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 7

19 BJT-CC & MOS-CD Transfer function v o v i (s) = g m R L + R L r in + g m R L + R S + R L r in p = g m + r, z = in R C in C in R S = + r x R L = r o g mb R = r in R S + R L + g m R L s z s p ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 8

20 BJT-CC Poles & zeros z = g m + r π C π g m C π ω T p = R C π, R = r π R S + R L + g m R L R S = + r b, R L = r o Typically, z is slightly larger than p. If g m R L and R S R L, then R /g m and p ω T. If R S is large (compared to R L ), then p will be significantly less than ω T. ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 9

21 MOS-CD Poles & zeros z = g m C gs ω T p = R C gs, R = + R L + g m R L R L = r o g mb Typically, z is slightly larger than p. If g m R L and R L, then R /g m and p ω T. If is large (compared to R L ), then p will be significantly less than ω T. ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 20

22 BJT-CC & MOS-CD Input impedance r x r x Z i r in v C in g m v Z i (+ g ) m r in Cin +g m Z i = r x + R sc + R L R = ( + g m R L )r in, C = R L = r o g mb C in + g m R L ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 2

23 BJT-CC & MOS-CD Input impedance BJT: Z i = r b + R sc + R L R = ( + g m R L )r π, C = R L = r o C π + g m R L MOS: Z i = sc + R L C gs C = + g m R L R L = r o g mb ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 22

24 BJT-CC & MOS-CD Output impedance v o r in v C in g m v Z o v = z in z in + R v o, z in = r in S sc in Z o = (z in + R S ) z in + R S R L g m z = in R S = + r x, R L = r o g mb z in + R S + g m z in R L ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 23

25 BJT-CC & MOS-CD Output impedance Z o = R L r in + R S + sc in (R S r in) + g m r in + sc in r in g m > R S g m < R S g m = R S g m Z o is capacitive Z o is inductive Z o is resistive Practical design goals: r x, g m = ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 24

26 BJT-CC & MOS-CD Output impedance BJT: Z o = r o r π + + r b β + + sc π (( + r b ) r π ) + sc π r π g m MOS: Z o = r o g mb + sc gs g m + s C gs g m ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 25

27 BJT-CB & MOS-CG Small-signal circuit V i V o V i V o g mb v g m v i o v o v i =i i v r in C in C f ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 26

28 BJT-CB & MOS-CG Transfer function i o i i (s) = K s p v o v i (s) = K s p s p 2 K = g m + g mb g m + g mb + + r in g m + g mb + + R p = S r in, p 2 = C in C f ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 27

29 BJT-CB & MOS-CG Poles BJT: v o v i (s) = g m g m α + s p s p 2 p = g m α + C π, p 2 = C µ MOS: v o v i (s) = g m + g mb g m + g mb + s p s p 2 p = g m + g mb + C gs, p 2 = C gd ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 28

30 Multistage Amplifiers Dominant-pole approximation A(s) = = K + b s + b 2 s b n s n s p K s p 2 s p n If p p 2, p 3,... then b p b = The higher 3-dB frequency is n i= p i, A(jω) + K ω p 2 ω H p b ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 29

31 Open-Circuit Time Constant Analysis Also known as Zero-Value Time Constant Analysis. Can be used to estimate the higher 3-dB frequency (ω H ). C C n C2 Circuit with no capacitors C 3 Circuit with no capacitors v k C k C 4 ik R ko R ko = v k, T ko = R ko C k i k n b = R koc k = R o C + R 2o C R no C n k= ω H p b T ko k ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 30

32 Short-Circuit Time Constant Analysis Can be used to estimate the lower 3-dB frequency (ω L ) of ACcoupled amplifiers. C C n C2 Circuit with no capacitors C 3 Circuit with no capacitors v k C k C 4 ik R ks R ks = v k, τ ks = R ks C k i k ω L n k= τ ks ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 3

33 Short-Circuit Time Constant Analysis Can be used to estimate the nondominant pole (p 2 ) in DCcoupled amplifiers that have only two widely-spaced real poles. C 2 C Circuit with no capacitors Circuit with i v no capacitors R s R ks = v k i k, τ ks = R ks C k, k =, 2 p 2 2 k= τ ks ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 32

34 Cascode Frequency Response v o v o Q 2 M 2 v i Q v i M ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 33

35 Differential Pair Current mirror load V DD M 3 M 4 V o V M M 2 id V id I T 2 2 C x v gs4 gm3 i o g m4 v gs4 V id 2 v g m v g m2 v 2 v 2 V id 2 ECEN 326 Electronic Circuits - Aydın İ. Karşılayan - Frequency Response 34