Common Drain Stage (Source Follower) Claudio Talarico, Gonzaga University Common Drain Stage vgs = vi - vo vbs = - vo VDD RS VvIiN C C+C gd gdg b B&D vi G vs V vOoU T + VS C r gmvgs -gmbvo vgs gs o IB RL CL - vo S V B RL Csb+CL EE 303 – Common Drain Stage 2 CD Bias Point VDD § Assume VB=VOUT, so ID=IB RS VIN VOUT = VIN −VGS I VOUT D VGS = VT + VS 0.5COXW / L I R B L V V PHI V PHI T = T 0 +γ ( + OUT − ) VB VDS = VDD −VOUT = VDD −VIN +VGS § For M1 to be in saturation VDS > VOV = VGS +VT ! VDD −VIN +VGS > VGS +VT ! This is almost always the case VIN < VDD +VT in practical realizations EE 303 – Common Drain Stage 3 I/O DC characteristic (1) Example: DC Transfer Function − 1 um Technology 5 VIN = 2.5V; I1=400µA; 4.5 VDD=5V; W/L=100µm/1µm Vout 4 Vth M1 triode 3.5 VDD-Vth ≈ 3.43 V 3 Source: Razavi [V] 2.5 out V 2 M operation 1 1.5 6 1 5 0.5 Vds=Vdd−Vout 0 4 Vov=Vin−Vout−Vth 0 1 2 3 4 5 6 7 8 V [V] in ≅ 3 AV (@ VIN = 2.5V) 0.821 M1 sat. Math “artifact” due to ideal current source 2 (a current source can take any voltage value across it !!) 1 M1 triode § Vout(min) ≈ 0 0 0 1 2 3 4 5 6 7 8 § Vout(max) ≈ VDD-Vth V [V] in EE 303 – Common Drain Stage 4 I/O DC characteristic (2) Example: DC Transfer Function − 1 um Technology 5 VIN = 2.5V; I =400 A; 1 µ 4.5 VDD= 5V; V = 0.9V; 4 I1 B W/L=100µm/1µm; 3.5 3 Vout=Vds2 element 0:m1 0:m2 [V] Vov2 model 0:simple_n 0:simple_n 2.5 region Saturati Saturati out Vds1 id 452.1261u 452.1261u V 2 Vov1 ibs -13.0315f 0. ibd -50.0000f -13.0315f 1.5 vgs 1.1968 900.0000m vds 3.6968 1.3032 vbs -1.3032 0. 1 vth 833.4784m 500.0000m vdsat 363.3703m 400.0000m 0.5 vod 363.3703m 400.0000m beta 6.8484m 5.6516m 0 gam eff 600.0000m 600.0000m 0 1 2 3 4 5 6 7 8 V [V] gm 2.4885m 2.2606m in gds 33.0095u 40.0000u gmb 514.7852u 758.2384u M off 2 M2 triode M2 sat M2 sat cdtot 72.3963f 93.2122f M sat M sat cgtot 256.5245f 256.4846f 1 1 M1 sat M1 triode cstot 246.1466f 286.3341f cbtot 66.1318f 128.5634f § Reduced output (and input) swing cgs 203.3341f 203.3341f - V (max) = V – V cgd 51.1337f 50.3996f out DD OV1 - Vout(min) = VOV2 * measurement EE 303 – Common Drain Stage 5 av0= 808.9285m CD Voltage Transfer ' 1 $ v % sC sC " v sC g v v 0 o % Ltot + gs + " − i gs − m ( i − o )= & RLtot # vi v g + sC o = m gs + 1 g v vi v Cgs m gs g + sC + sC + gs m gs Ltot R - Ltot LHP C +C v gd gb o zero C R Ltot Ltot sC 1+ gs v g g o = m ⋅ m = 1 vi s(Cgs +CLtot ) gm + 1+ RLtot 1 gm + 1 RLtot CLtot = CL + Csb RLtot = RL || || ro g s mb 1− = a ⋅ z v0 s ≅ 1 1− often RLtot /gmb p EE 303 – Common Drain Stage 6 Low Frequency Gain g 1 a = m R = R || || r v0 1 Ltot L o gmb gm + RLtot § Interesting cases V DD – Ideal current source; PMOS with source tied to body; no load resistor; RL=∞, ro=∞, gmb= 0 Vo Vi C L a =1 Yin v0 V DD – Ideal current source; NMOS; no load resistor;! V i RL=∞, ro=∞, gmb≠0 V o gm av0 = (typically ≅ 0.8) I R C B L L gm + gmb – Ideal current source, PMOS with source tied to body; load resistor r =∞, g =0, R finite g o mb L a = m v0 1 gm + EE 303 – Common Drain Stage 7 RL Low frequency input and output resistances Rin Rout RS vin vout vs gmvin ro 1/gm 1/gmb RL av0= gm / (g’m+1/ro+1/RL) § Rin = ∞ § Rout = ro || (1/g’m) EE 303 – Common Drain Stage 8 High Frequency Gain gm av0 = g'm +1/ ro +1/ RL s 1 1− g g + vo z m m av (s)= = av0 ⋅ z = − RLtot v s C p = − i 1− gs C + C p gs Ltot § Three scenarios: The presence of a LHP zero leads to the possibility that the pole and zero |z|<|p| |z|>|p| |z|=|p| will provide some degree of cancellation, |a (s)| |a (s)| |a (s)| v v v leading to a broadband response av0 av0 av0 f f f (infinite bandwidth ?!?) EE 303 – Common Drain Stage 9 CD Input Impedance Consistent with insight from § By inspection: Miller Theorem Hint: Yin = sCgd + sCgs (1− av (s)) i=Cgs(vi-vo) vi Yin + § Gain term av(s) is real and close to unity C gmvgs vgs gs up to fairly high frequencies - C +C v gd gb o § Hence, up to moderate frequencies, we CLtot RLtot see a capacitor looking into the input – A fairly small one, Cgd, plus a fraction of Cgs EE 303 – Common Drain Stage 10 CD input impedance for PMOS stage (with Body-source tie) VDD § gmb generator inactive – Low frequency gain very close g r >> 1 IB to unity m o g vOVUT m out av0 = ≅1 Cgs 1 g + CL m r Cbsub o vVIinN § Very small input capacitance Cgd CCin @ ≈ C Cgd in gd Yin = sCgd + sCgs (1− av (s)) Yin ≅ sCgd for av=1 (Vout=Vin) no current flows through Cgs(perfect bootstrap) § The well-body capacitance Cbsub can be large and may significantly affect the 3-db bandwidth EE 303 – Common Drain Stage 11 CD Output Impedance (1) § Let's first look at an analytically simple case – Input driven by ideal voltage source 1 1 Zout = + gm + gmb s(Cgs + Csb ) C gmvgs vgs gs - vo Cgd+Cgb Zout Csb 1/gmb ZL AC shorted Low output impedance • Resistive up to very high frequencies YL=sCL+1/RL EE 303 – Common Drain Stage 12 CD Output Impedance (2) § Now include finite source resistance vg Ri g (v -v ) Cgs m g o Zx Zout Cgd+Cgb vo i x Csb 1/gmb ZL Neglect Cgd Neglecting Cgd " v % v R i = v − v g + sC = v 1− g g + sC g ≅ i x ( o g )( m gs ) o $ '( m gs ) 1 # vo & vo + Ri " % sCgs $ ' 1+ sR C 1+ sR C vo i gs 1 $ i gs ' Zx = ≅ = i g + sC g $ sCgs ' x m gs m $ 1+ ' # gm & EE 303 – Common Drain Stage 13 CD Output Impedance (3) 1 1+ sRiCgs Z ≅ ( ) x g " sC % m $1+ gs ' # gm & NOTE: Typically 1/gm is small, § Two interesting cases so this can happen !! R < 1/g i m Ri > 1/gm |Zx(s)| |Zx(s)| 1/gm 1/gm f f Inductive behavior! EE 303 – Common Drain Stage 14 Equivalent Circuit for Ri > 1/gm for s 0 Z 1/ g 1 (1+ sRiCgs ) = ⇒ x = m Zx ≅ g " sC % for s → ∞ ⇒ Zx = Ri m $1+ gs ' # gm & Z Z x out 1 R1 || R2 = R1 gm for s = 0 ⇒ Zx = R1 || R2 R2 Csb 1/gmb R = R for s → ∞ ⇒ Z = R 2 i x 2 L R2C L = i gs gm Ri −1 L 1+ (R + sL)R R R R Z = 1 2 = 1 2 1 x R + R + sL R + R L 1 2 1 2 1+ R1 + R2 § This circuit is prone to ringing! – L forms an LC tank with any capacitance at the output – If the circuit drives a large capacitance the response to step-like signals will result in ringing EE 303 – Common Drain Stage 15 Inclusion of Parasitic Input Capacitance* What happens to the output impedance if we don’t neglect Ci=Cgd ? * Hint: replace Ri with 1+ sR C +C Ri 1 ( i ( gs i )) Zi = Zx = Ri + sCiRi gm ! sCgs $ #1+ &(1+ sRiCi ) " gm % € 1 g 1 1 1 g < m < < < m R C +C R C C Ri (Cgs +Ci ) Cgs RiCi i ( gs i ) i i gs |Z (s)| |Zx(s)| x 1/gm 1/gm f f EE114 EE 303 – Common Drain Stage 16 Applications of the Common Drain Stage § Level Shifter § Voltage Buffer § Load Device EE 303 – Common Drain Stage 17 Application 1: Level Shifter Vi=VGS +Vo VDD Vo=Vi – VGS= Vi – (Vt+VOV) Vi VGS=Vt+Vov ≅ const. Vo IB § Output quiescent point is roughly Vt+Vov lower than input quiescent point § Adjusting the W/L ratio allows to “tune” Vov (= the desired shifting level) EE 303 – Common Drain Stage 18 Why is lowering the DC level useful ? § When building cascades of CS and CG amplifiers, as we move along the DC level moves up § A CD stage is a way to buffer the signal, and moving down the DC level EE 303 – Common Drain Stage 19 Application 2: Buffer VDD VVBB1 IB1 RD (large) M1 vx Rout vVooutut Vvinin MX I RL M2 B2 (small) VB2 § Low frequency voltage gain of the above circuit is ~gmRbig – Would be ~gm(Rsmall||Rbig) ~ gmRsmall without CD buffer stage § Disadvantage Vout (max) = VDD −VOV1 – Reduced swing Vout (min) = VOV 2 EE 303 – Common Drain Stage 20 Buffer Design Considerations VDD V § Without the buffer the minimum VBB1 allowable value of Vx for Mx to IB1 RD (large) M1 remain in saturation is: VX > VGSX – Vthx vx Rout Vx vVououtt § With the buffer for M2 to remain in sat.