Multiple stage amplifiers

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1 Multple stage amplfers Ams: Examne a few common 2-transstor amplfers: -- Dfferental amplfers -- Cascode amplfers -- Darlngton pars -- current mrrors Introduce formal methods for exactly analysng multple stage amplfers Imperal College London EEE

2 Two stage BJT amplfers We study them separately because they very often appear as buldng blocks. There are 9 possble cascades of 2 sngle stage transstor amplfers. We wll study the shaded ones. BJT Name st Stg 2nd Stg (voltage amp) CE CE cascode CE CB (op-amp) CE CC (current buffer) CB CE (current buffer) CB CB (Not common) CB CC (Not common) CC CE dfferental amp CC CB darlngton CC CC Comments Hgh Voltage gan Hgh bandwdth Hgh Z n low Z out Hgher Z out than CB/CG SecondstagetomproveonCB/CG Not common Instead of CE, offers hgher Z n Hgh voltage gan and bandwdth Hgh current gan Imperal College London EEE 2

3 Dfferental amplfer Half crcut (.e. drven from one sde) s CC followed by CB Very wde frequency response Extremely hgh voltage gan Imperal College London EEE 3

4 Cascode amplfer Wdeband voltage amplfer CE stage operates at gan=-, mnmsng mller loadng of nput. CB gves all the voltage gan, actng as transmpedance of value Z L The cascode has a much hgher output mpedance (other than Z L ) than the CE amplfer (the common emtter Early resstance acts as seres-seres feedback to the common base wth loop gan =g m R CE ) Imperal College London EEE 4

5 Darlngton par The darlngton par s a hgh gan power amplfer t has: Unty voltage gan Hgh current gan equal to the product of the two transstor current gans Often used as a sngle transstor for hgher beta. But : has hgh nput DC voltage drop Good frequency response due to the absence of shunt Mller feedback. However, seres Mller feedback ntroduces tendency for nstablty when drvng capactve loads. Imperal College London EEE 5

6 Current mrrors Use one transstor wth unty feedback as a transmpedance amplfer to measure the V BE requred for a gven current. Use a second transstor as transconductor to create a copy of the nput current Can make a current amplfer by usng larger output transstor. Current gan s n error due to base currents (.e fnte current gan) No DC gan error n FET mrrors (remember the AC current gan of a FET scales as the nverse of frequency!) Man source of error transstor msmatch V BE msmatch at a constant current (BJT) V T msmatch n FET AC analyss as n CE amplfer wth extra source admttance due to nput transstor Current mrrors are used for DC basng mult-stage amplfers Current mrrors often used load to a dfferental amplfer to turn the dfferental amplfer nto a Smple current Mrror dfferental transconductor. Imperal College London EEE 6

7 Improved current mrrors The buffered mrror The CC amplfer feedng the bases reduces current gan error The Wlson Mrror has hgh output Z, snce output stage s a cascode amplfer Imperal College London EEE 7

8 Scalng Mrrors: The Wdlar mrror (a) (b) (c) The Wdlar scalng mrror s often used as fxed scalng current source (a) Can be made as a buffered or a Wlson source (c) A feedback resstor can be added on the nput sde turnng t nto a transconductor (b) A base resstor as shown can provde beta compensaton (.e. ntroduce a zero n the frequency response (c) Imperal College London EEE 8

9 Some more mrrors (a) (a) Buffered Wdlar mrror (b) The gm-compensated mrror (b) Imperal College London EEE 9

10 Current mrror as a dfferental amp load The current mrror maps the left sde current dfferental nto the rght sde. The large sgnal response of ths crcut s V out =tanh(v + -V - ) Ths crcut (a 3 stage amplfer! Why?) Ths crcut It has extremely hgh voltage gan: A V s of the order of V A /V th Ths crcut s also used for mxers f a transconductor s used n the place of the tal current source. There s no Mller effect on the left half crcut If ths crcut drves a current snk at the output there s no Mller effect on the rght half crcut ether! The dff-amp has an extremely wde frequency response. Ths s partly a consequence of the resstve mpedance match between the output of the frst stage (emtter of Q)and nput of the second stage (emtter of Q2). Q Q2 Imperal College London EEE 0

11 Two stage FET amplfers The analogy we observed between sngle stage BJT and FET amplfers apples, to two stage amplfers. The correspondence s, as before, E S, B G, C D. The behavour of BJT and FET confguratons s very smlar, except for the dfference on the nput sde of the small sgnal equvalent crcut. A very useful possblty opens up: Use a FET for one stage and a BJT for the other. Mxed bpolar-fet two-stage combnatons try to explot the smaller nput admttance of FETs and the better frequency response and power handlng capablty of bpolars at the same tme. Ths approach gves rse to the BCMOS manufacturng technologes whch use FETs for nput stages and BJTs for output stages, especally lne drvers. Name (voltage amp) cascode (op-amp) (current buffer) (current buffer) (Not common) (Not common) dfferental amp darlngton FET Comments st Stg 2nd Stg CS CS Hgh Voltage gan CS CG Hgh bandwdth CS CD Hgh Z n low Z out CG CS Hgher Z out than CB/CG CG CG Second stage to mprove on CB/CG CG CD Not common CD CS Instead of CE, offers hgher Z n CD CG Hgh voltage gan and bandwdth CD CD Hgh current gan Imperal College London EEE

12 - - Multstage amplfers Multstage amplfers are dffcult to compute f the components are not unlateral. For unlateral amplfers thngs are smple. We multply gans wth approprate voltage dvders. V V2 VL Rs Vs RIN + - ROUT A V RIN2 + - RO2 A2 V2 RL Source Amp Amp2 Load V = A A, Y =, x n, n2, L V RY R Y R Y R L 2 x s + s n + out n2 + o2 L x For non-unlateral amplfers: The nput mpedance of each stage depends on the nput mpedance of the next stage The output mpedance of each stage depends on the output mpedance of the precedng stage. Ths problem has a soluton but nvolves the soluton of sets of smultaneous quadratc equatons. { } Imperal College London EEE 2

13 Input - output mpedance of a loaded amplfer We calculate the nput mpedance of a voltage amplfer drvng a load Z L : = g v + g 2 2 = gv g2ylv2 2 = v2 g2v g22ylv2 2 v2y = L v g v g = g v Y = g v v = = + g Y 2 2 L 22 L Zn + g22yl v2 = g2v g+δgyl ( ) A smlar calculaton for the output mpedance of a voltage amplfer drven by a fnte mpedance Thevenn source Z S gves: = gv+ g22 = g( vs Z S) + g22 v = g v + g v2 = g2( vs Z S) + g222 v v Z = s S Z = dv / d = out 2 2 g 22 +Δ + g Z g Z S S Imperal College London EEE 3

14 Gan of a fully loaded voltage amplfer Z S 2 VS G 22 v G v 2 G 2 V Y L G 2 2 We start wth the amplfer defnton, plus the source-load boundary condtons: = g v + g 2 2 v = g v + g v = v Z s = v Y 2 2 After some algebra we conclude that: ( )( ) s s 22 L 2 2 s L S 22 L g L s L v2 g2 g2 = =, Δ g = g g g g v + g Z + g Y g g Z Y + g Z + g Y +Δ Y Z s Imperal College London EEE 4

15 Cascade connecton: Transmsson Parameters In a cascade connecton, V of network X 2 = V 2 of network X I of network X 2 = -I 2 of network X We can defne a new set of parameters so that we have a smple way to calculate the response of cascades of amplfers. A sutable defnton s: v A B v = 2 C D 2 Wth ths defnton, the ABCD parameters of a cascade of two networks are found from the matrx product of the ndvdual ABCD matrces ports labelled for clarty): X X 2 X 3 =X X 2 v A B v2 = C D 2 v A B A2 B2 v3 v A3 B3 v3 v = 2 A2 B2 v3 C D C2 D 2 3 = C3 D 3 3 = 2 C2 D 2 3 Imperal College London EEE 5

16 Transmsson (or ABCD) parameters (2) The transmsson matrx elements are related to the 4 gans: v v A = = B= = v A B v2 v2 G 2 2 Y2 2= 0 v2= 0 = C D 2 C = = D= = v2 Z 2 2 H2 2= 0 v2= 0 A cascade of 2 amplfers has gans: A C D = C D C2 D = 2 CA2 DC 2 CB2 DD g z f f B A B A B AA + BC AB + BD g g y z g y y h = = y = = y z g g y h g y g g y z g y y h f f 2 f f 2 f f 2 f f 2 f f f 2 f f 2 f f 2 f f 2 f f 2 f f 2 f f 2 f f 2 = = z g h z f f 2 f f 2 z g h z h h z y h = = h z z g z y h h h h z y f f 2 f f 2 f f 2 f f 2 f f f 2 f f 2 f f 2 f f 2 f f 2 f f 2 Imperal College London EEE 6

17 Transmsson (or ABCD) parameters (3) Note the sgn of 2 and also the reverse sense of sgnal flow. The sgn s chosen so the ABCD matrx of a cascade of two networks s just the matrx product of the ndvdual ABCD matrces (compare ths to the messy loadng calculaton before!) The reverse sense of sgnal flow s to keep the matrx fnte f an amplfer s unlateral. The converson from, say, Y to ABCD follows the same logc as the Y(H) calculaton: v A B v 0 v A B 0 v = = 2 C D 2 Y Y 2 v 2 C D Y2 Y 22 v 2 A B Y C D Y v A B v = 2 C D 2 YY YY 22 =, Δ y = ΔY Y Remember that all ABCD parameters are nversely proportonal to the gans. Ths s the reason for formally choosng port 2 as the nput port. The ntutve choce of nput at port would make all parameters nversely proportonal to the reverse gans, whch are small, and usually not very accurately determned. Imperal College London EEE 7

18 Composton rules summary For the exact calculaton of crcut nterconnectons we can use 2-port matrx algebra: Y Y 2 Y +Y 2 G G 2 G +G 2 shunt-shunt: add Y matrces shunt-seres: add G matrces Z Z +Z 2 H H +H 2 Z 2 H 2 seres-seres: add Z matrces seres-shunt: add H matrces X X 2 X X 2 cascade connecton: multply ABCD matrces Imperal College London EEE 8

19 Multstage amplfers: summary Calculaton of the response of unlateral mult-stage amplfers s smple: Product of gans and voltage dvders. Calculaton of the response of non-unlateral multstage amplfers nvolves determnng for each stage: the effect of source mpedance on gan and output mpedance the effect of load mpedance of nput mpedance and gan Ths typcally leads to a set of smultaneous quadratc equatons. A conceptually smpler analyss method nvolves the transmsson or ABCD parameters whch allow to descrbe all the loadng effects of a non-unlateral cascade through a matrx product. Wth the ntroducton of ABCD parameters we have ntroduced smple ways to descrbe any connecton between 2-port crcuts. Imperal College London EEE 9

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