4-H- Parameter - Notes PDF

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H – Parameter model :→ The equivalent circuit of a transistor can be dram using simple approximation by retaining its essential features. → These equivalent circuits will aid in analyzing transistor circuits easily and rapidly.

Two port devices & Network Parameters:→ A transistor can be treated as a two part network. The terminal behaviour of any two part network can be specified by the terminal voltages V1 & V2 at parts 1 & 2 respectively and current i1 and i2, entering parts 1 & 2, respectively, as shown in figure.

Two port network

→ Of these four variables V1, V2, i1 and i2, two can be selected as independent variables and the remaining two can be expressed in terms of these independent variables. This leads to various two part parameters out of which the following three are more important. 1. Z – Parameters (or) Impedance parameters 2. Y – Parameters (or) Admittance parameters 3. H – Parameters (or) Hybrid parameters. Hybrid parameters (or) h – parameters:→ If the input current i1 and output Voltage V2 are takes as independent variables, the input voltage V1 and output current i2 can be written as V1 = h11 i1 + h12 V2 i2 = h21 i1 + h22 V2 The four hybrid parameters h11, h12, h21 and h22 are defined as follows. h11 = [V1 / i1] with V2 = 0 = Input Impedance with output part short circuited. h22 = [i2 / V2] with i1 = 0 = Output admittance with input part open circuited.

h12 = [V1 / V2] with i1 = 0 = reverse voltage transfer ratio with input part open circuited. h21 = [i2 / i1] with V2 = 0 = Forward current gain with output part short circuited.

The dimensions of h – parameters are as follows: h11 - Ω h22 – mhos h12, h21 – dimension less. → as the dimensions are not alike, (ie) they are hybrid in nature, and these parameters are called as hybrid parameters. I = 11 = input ; 0 = 22 = output ; F = 21 = forward transfer ; r = 12 = Reverse transfer.

Notations used in transistor circuits:hie = h11e = Short circuit input impedance h0e = h22e = Open circuit output admittance hre = h12e = Open circuit reverse voltage transfer ratio hfe = h21e = Short circuit forward current Gain.

The Hybrid Model for Two-port Network:-

V1 = h11 i1 + h12 V2 I2 = h1 i1 + h22 V2 ↓ V1 = h1 i1 + hr V2 I2 = hf i1 + h0 V2

The Hybrid Model for Two-port Network

Transistor Hybrid model:Use of h – parameters to describe a transistor have the following advantages. 1. h – parameters are real numbers up to radio frequencies . 2. They are easy to measure 3. They can be determined from the transistor static characteristics curves. 4. They are convenient to use in circuit analysis and design. 5. Easily convert able from one configuration to other. 6. Readily supplied by manufactories.

CE Transistor Circuit

To Derive the Hybrid model for transistor consider the CE circuit shown in figure.The variables are iB, ic, vB(=vBE) and vc(=vCE). iB and vc are considered as independent variables. vB= f1(iB, vc ) ( 1) iC= f2(iB, vc ) ----------------------(2)

Then ,

Making a Taylor’s series expansion around the quiescent point IB, VC and neglecting higher order terms, the following two equations are obtained. ΔvB =

(∂f /∂i )

ΔiC =

(∂f /∂i )

1

2

Vc

B

Vc

B

(

)

(

)

. ΔiB + ∂f1/∂vc

. ΔiB + ∂f2/∂vc

IB

IB

. ΔvC ---------------(3) . ΔvC ----------------(4)

The partial derivatives are taken keeping the collector voltage or base current constant as indicated by the subscript attached to the derivative. ΔvB , ΔvC , ΔiC , ΔiB represent the small signal(increment) base and collector voltages and currents,they are represented by symbols vb , vc , ib and ic respectively. Eqs (3) and (4) may be written as

Where

Vb = hie ib + hre Vc ic = hfe ib + hoe Vc hie =(∂f1/∂iB) c = (∂vB/∂iB) c = (ΔvB /ΔiB) c = (vb / ib) c V

hre =(∂f1/∂vc)I = B

V

(∂v /∂v ) B

c

hfe =(∂f2/∂iB) c =

(∂i /∂i )

hoe= (∂f2/∂vc)I =

(∂i /∂v )

V

B

c

Vc

B

c

c

V

IB

V

= (ΔvB /Δvc) I = (vb /vc) I B

B

= (Δic /ΔiB) c = (ic / ib) c

IB

V

V

= (Δic /Δvc) I = (ic /vc) I B

B

The above equations define the h-parameters of the transistor in CE configuration.The same theory can be extended to transistors in other configurations.

Hybrid Model and Equations for the transistor in three different configurations are are given below.

Find the (i) input impedance and (ii) voltage gain for the circuit shown in Fig. 24.9.

Fig. 24.9 Solution. The h parameters of the circuit inside the box are the same as those calculated in example 24.1 i.e. h h 11 = 10 ; 21 = − 1 h h 12 = 1 and 22 = 0.2 (i) Input impedance is given by : 1×− h h h 12 21 1 Z = 11 − = 10 − in

h 22

+

1

0.2 + 1

rL 5 = 10 + 2.5 = 12.5 Ω By inspection, we can see that input impedance is equal to 10 Ω plus two 5 Ω resistances in parallel i.e. = 10+ 5 ||

Z

5

in

5× 5 = 12.5 Ω = 10+ 5+ 5 −h

(ii)

21

Voltage gain, Av =

Z

h +

in

22

= 12.5

1

1

0.2 +  1

=1

5

5

rL Example 24.4. A transistor used in CE arrangement has the following set of h parameters when

the d.c. operating point is = 10 volts and VCE IC = 1 mA : = 2000 Ω; −3 −4 h = 10 ; h = 50 h =10 mho; h ie

re

oe

fe

Determine (i) input impedance (ii) current gain and (iii) voltage gain. The a.c. load seen by the transistor is rL = 600 Ω. What will be approximate values using reasonable approximations? Solution. (i) Input impedance is given by : −3 2000 10 × .... h h 50 (i) Z = h − re fe = − −4 in ie h +1 10 + 1 oe 60 r 0 L 2000 − 28 = 1972 = Ω The second term in eq. (i) is quite small as compared to the first. = 2000 Z jh Ω in ie ∴ h fe 50 A 1 + hoe × 1 + (600 × 10−4 )= 47 (ii) Current gain, i = rL = If hoe r L...