Differential Amplifier Common & Differential Modes

Differential Amplifier Common & Differential Modes Common & Differential Modes BJT Differential Amplifier Diff. Amp Voltage Gain and Input Impedance Small Signal Analysis Differential Mode Small Signal Analysis Common Mode 1

Common and Differential Modes Consider a circuit with the two-port configuration shown Define (convention) the voltages: ±av 1 I Z Z 3 V V d =V 1 V c = V 1 V V c = common mode voltage V d = differential mode voltage ±a V 1. Let V 1 = V = V => V c = V & V d = 0. Let V 1 = -V = V => V c = 0 & V d = V

Replace V 1, V with CM and DM Sources Simultaneous Equations: ±a V d I Z Z 3 V 1 V =V c V 1 V =V d I V 1 - V d ±a ±. V c Definition V V c = V 1 V V d =V 1 V Adding: V 1 = V c V d V 1 =V c V d Subtracting: V =V c V d V =V c V d V c common to V 1 & V ; V d is split between V 1 & V s.t. difference V 1 - V = V d 3

Common and Differential Mode Currents Simultaneous Equations: I = V d ±. I Z Z 3 I 3 = I I = I d Adding: = I d ±. ±. V c - V d = / I d Subtracting: I = I d Define (convention): = I I d = I I = I d I 3 = I = 4

CM-DM Circuit Description ±. V d I I d = - I Z3 1. Voltage sources redefined as common and differential mode quantities.. Differential mode currents take blue path. ±. ±. V c - V d Z = I 3. Common mode current takes red path. OBSERVATIONS i. No DM I d flows through Z 3. ii. No CM flows around, Z loop = / I d I = I d 5

= I d ±. V d ESE319 Introduction to Microelectronics Analyze Circuits by Superposition Balanced Circuit Differential Mode (V C = 0) -I = I d ±. - V d V Z1 - Z - V Z balanced circuit => V x Z3 = I = 0 =Z =Z = I = I d I d =0 = I = I d = V d V x =0 V x =0 V d V d Z V d V x = V d Z Z i n dm = V d I d = Z Z = V x Z =0 NOTE: If Z = Z, then 0 => V x 0. 6

I Analyze Circuits by Superposition Balanced Circuit Common Mode (V d = 0) I d = I = 0 Z Z3 = V c Z Z 3 = V c Z Z 3 I d = I = =0 I d=0 ±. V c Z i n cm = V c = Z Z 3 balanced circuit => =Z =Z 7

Quick Review <=> I I Definitions: V c = V 1 V V d =V 1 V = I I d = I All V's & I's have differential & common mode components V 1 =V c V d V =V c V d = / I d I = I d 8

Quick Review DM (V c = 0) CM (V d = 0) = I d V V x = 0 x =? I - I = I d Z i n dm = V d I d = Z = I I d = I = / I d I = I d Z i n cm = V c = Z Z 3 9

Summary In a balanced differential circuit ( = Z = Z): 1. Differential mode voltages result in differential mode currents.. Common mode voltages result in common mode currents. The differential mode input impedance of a balanced circuit is: Z i n dm = Z = Z The common mode input impedance of a balanced circuit is: Z i n cm = Z Z 3 = Z Z 3 10

BJT Differential Amplifier Bias View I C = m m I B R B1 R C1 I E I E R C R B I B Q1=Q R C1 =R C =R C R B1 =R B =R B balanced circuit Collector bias path inherently common mode. I B = m 1 m I E = m I C = m m Choose m and R C for approximate ½ V CC drop across R C. 11

Voltage Gain & Input Impedance r in dm = v i dm i b dm v i-dm v i-dm v i- dm i B1-dm v C1-dm R B1 r o R C1 - vo-dm I R C v C-dm i B-dm R B r in cm = v i cm v i-cm i b cm v C1-cm i B1-cm - R B1 r o R C1 - vo-cm I = I CM R C v C-cm i B-cm R B - r in-dm Single-ended outputs: v c1-dm, v c-dm r in-cm Differential output: v o-dm = v c-dm - v c1-dm Single-ended outputs: v c1-cm, v c-cm Differential output: v o-cm = v c-cm - v c1-cm (diff) A v dm = v (s-e) o dm A v cm = v o cm A v v dm1, = v (diff) (s-e) c1, dm i dm v i dm v i cm A v cm1, = v c1, cm v i cm 1

BJT Differential Amplifier Small-signal View i c1 i c Z V x R B1 R C1 βi b1 r e1 V x r e R C βi b R B v i-dm Z 3 -v i-dm v i-dm i b1 i e1 r o i e i b v i-dm v i-cm r e1 =r e =r e R C1 =R C =R C R B1 =R B =R B v i-cm I CM current source output impedance i e1 =i edm i ecm & i e = i edm i ecm NOTE: 1. r o for amplifier Q1 & Q is ignored.. v i-dm and v i-cm are ac small signals =Z = 1 r e Z 3 = 1 r o 13

Balanced circuit => ESE319 Introduction to Microelectronics Superposition Small-signal Analysis Differential Mode (v i-cm = 0) R C1 =R C =R C, R B1 =R B =R B, r e1 =r e =r e, 1 = = i b-dm ib1i b i i c-dm c R C βi b R B r e - v o-dm i c-dm R C v x r e i e-dm i b -dm i b R B v i-dm i e i e v i-dm r o i e-dm i c βi b i e1 =i e =i e,i b1 =i b =i b,i c1 =i c =i c DM Path (ignoring both R B ): v i dm =i e dm r e i e dm r e v i dm vi dm = r e i e dm = 1 r e i b dm =Z = 1 r e i e1 dm =i e dm =i e1 =i e i b1 dm =i b dm =i b1 =i b i c1 dm =i c dm =i c1 =i c Z 3 = 1 r o i e dm=i e dm= i e= i e i b dm =i b dm = i b = i b i c dm =i c dm = i c = i c.=r in dm i b dm r i n dm = 1 r e Recall: Z i n dm = Z 14

i b-dm i b R B v i-dm ESE319 Introduction to Microelectronics Superposition Small-signal Analysis Differential Mode (v i-cm = 0) cont. i c i e-dm Balanced circuit R C i e i c-dm βi b-dm i e1 dm =i e dm =i e1 =i e i b1 dm =i b dm =i b1 =i b i c-dm R C i c v o dm =v c dm v c1 dm i b-dm v o dm = R C i b dm R C i b dm - v o-dm i b v c dm v i b dm = v c1 dm βi b-dm i dm 1 r e v x r e R B 1 r e i e v i v o dm = R i-dm C v r i dm o e-dm 1 r e DM Differential voltage gain: A v dm = v o dm = R C R C i e dm= i e dm=i e=i e v i dm 1 r e r e i b dm = i b dm =i b =i b DM Single-ended voltage gains: i c1 dm =i c dm =i c1 =i c i c dm = i c dm =i c =i c i c dm = i b dm A v dm = A v dm1 = v c dm v i dm = R C 1 r e R C r e 15

R B i b-cm ESE319 Introduction to Microelectronics Superposition Small-signal Analysis Common Mode (v i-dm = 0) i c-cm - βi b-cm r e =Z = 1 r e i cm =i e cm =i e1 =i e Balanced circuit R C v o-cm i e-cm icm i cm r o i c-cm r e i cm v i-cm R C i e-cm βi b-cm i b-cm R B Z 3 = 1 r o i cm =i e cm =i e =i e CM path: both r e are in parallel v i cm =[r e r e r o ]i cm i cm = v i cm v i cm r e r r o o i cm =i e cm = 1 i b cm v i cm =i b cm 1 r e r o r in cm = v i cm i b cm = 1 r e r o 1 r o i b1 cm =i b cm =i b1 =i b i c1 cm =i c cm =i c1 =i c i b cm =i b cm =i b =i b i c cm =i c cm =i c =i c Recall: Z i n cm =Z Z Z 3 = Z Z 3 16

R B i b-cm ESE319 Introduction to Microelectronics Superposition Small-signal Analysis Common Mode (v i-dm = 0) Balanced circuit i c-cm R C i e-cm - βi b-cm v o-cm i c-cm r e r e βi b-cm r o i cm i cm i cm R C i b-cm i e-cm R B v o cm =v c cm v c1 cm v o cm = R C i b cm R C i b cm =0 v i cm v i cm i b cm = 1 r o e r 1 r o v c cm =v c1 cm = R C i b cm = R C v 1 r i cm o i c dm = i b dm i cm =i e cm =i e1 =i e i b1 cm =i b cm =i b1 =i b i c1 cm =i c cm =i c1 =i c v i-cm i c dm = i b dm i cm =i e cm =i e =i e i b cm =i b cm =i b =i b i c cm =i c cm =i c =i c CM Differential voltage gain: A v cm = v o cm v i cm =0 CM Single-ended voltage gains: A v cm =A v cm1 = v c1 cm = R C R C v i cm 1 r o r o 17

Summary Differential mode: r i n dm = 1 r e Differential DM Voltage gain: A v dm = v o dm v i dm R C r e Single-Ended DM Voltage gain: Common mode: r i n cm = 1 r e r o 1 r o Differential CM Voltage gain: A v cm = v o cm v i cm =0 Single-Ended CM Voltage gain: A v dm1 = A v dm = v c1 dm v i dm R C r e A v cm1 =A v cm = v c1 cm v i cm R C r o 18