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The partial-derivative de nitions of the CB h-parameters are: Input resistance Reverse voltage ratio Forward current gain Output admittance
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@vEB % vEB hib  @iE Q iE Q @v vEB hrb  EB % @vCB Q vCB Q @i i hfb  C % C @iE Q iE Q @i iC hob  C % @v v
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CB Q CB Q
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6:11 6:12 6:13 6:14
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A small-signal, h-parameter equivalent circuit satisfying (6.9) and (6.10) is shown in Fig. 6-1(b) Common-Collector Ampli er The common-collector (CC) or emitter-follower (EF) ampli er, with the universal bias circuitry of Fig. 6-2(a), can be modeled for small-signal ac analysis by replacing the CE-connected transistor with its h-parameter model, Fig. 6-1(a). Assuming, for simplicity, that hre hoe 0, we obtain the equivalent circuit of Fig. 6-2(b).
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ic + hfe ib RE
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R1R2 R1 + R 2
_ a C (b) ib hie b
R1R2 R1 + R2 C (c)
(hfe + 1)RE
Le _
Fig. 6-2 CC ampli er
An even simpler model can be obtained by nding a Thevenin equivalent for the circuit to the right of a; a in Fig. 6-2(b). Application of KVL around the outer loop gives v ib hie ie RE ib hie hfe 1 ib RE The Thevenin impedance is the driving-point impedance: v RTh hie hfe 1 RE ib 6:15
6:16
SMALL-SIGNAL MIDFREQUENCY BJT AMPLIFIERS
[CHAP. 6
The Thevenin voltage is zero (computed with terminals a; a open); thus, the equivalent circuit consists only of RTh . This is shown, in a base-current frame of reference, in Fig. 6-2(c). (See Problem 6.13 for a development of the CC h-parameter model.)
TEE-EQUIVALENT CIRCUIT
The tee-equivalent circuit or r-parameter model is a circuit realization based on the z parameters of 1. Applying the z-parameter de nitions of (1.10) to (1.13) to the CB small-signal equivalent circuit of Fig. 6-1(b) leads to z11 hib z12 z21 z22 hrb hob hfb hob 1 hob hrb hfb hob 6:17 6:18 6:19 6:20
(See Problem 6.17.) Substitution of these z parameters into (1.8) and (1.9) yields   hrb hfb h veb hib ie rb ic hob hob hfb 1 vcb i ic hob e hob If we now de ne rb hrb hob hrb 1 hfb hob
6:21 6:22
6:23 6:24 6:25 6:26
re hib rc
1 hrb hob hfb hrb 0 1 hrb then (6.21) and (6.22) can be written veb re rb ie rb ic and vcb 0 rc rb ie rb rc ic
6:27 (6.28)
Typically, 0:9 > hfb > 1 and 0 hrb ( 1. Letting hrb % 0 in (6.26), comparing (6.13) with (3.1) while neglecting thermally generated leakage currents, and assuming that hFB hfb (which is a valid assumption except near the boundary of active-region operation) result in 0 % hfb 6:29
Then the tee-equivalent circuit or r-parameter model for CB operation is that shown in Fig. 6-3. (See Problems 6.3 and 6.5 for r-parameter models for the CE and CC con gurations, respectively.)
CHAP. 6]
SMALL-SIGNAL MIDFREQUENCY BJT AMPLIFIERS
= ie
ie re rb rc
Fig. 6-3
CONVERSION OF PARAMETERS
Transistor manufacturers typically specify hFE % hfe and a set of input characteristics and collector characteristics for either CE or CB connection. Thus the necessity arises for conversion of h parameters among the CE, CB, and CC con gurations or for calculation of r parameters from h parameters. Formulas can be developed to allow ready conversion from a known parameter set to a desired parameter set.
Example 6.1. Apply KVL and KCL to Fig. 6-1(a) to obtain veb g1 ie ; vcb and ic g2 ie ; veb . Compare these equations with (6.9) and (6.10) to nd the CB h parameters in terms of the CE h parameters. Use the typically reasonable approximations hre ( 1 and hfe 1 ) hie hoe to simplify the computations and results. KVL around the E; B loop of Fig. 6-1(a) (with assumed current directions reversed) yields veb hie ib hre vce But KCL at node E requires that ib ie ic ie hfe ib hoe vce 1 hoe i v ib hfe 1 e hfe 1 ce vce vcb veb Substituting (6.31) and (6.32) into (6.30) and rearranging give   1 hre hfe 1 hie hoe hie hie hoe veb ie hre vcb hfe 1 hfe 1 hfe 1 6:30
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