Microelectronics: Circuit Analysis and Design
Microelectronics: Circuit Analysis and Design
4th Edition
ISBN: 9780073380643
Author: Donald A. Neamen
Publisher: McGraw-Hill Companies, The
Question
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Chapter 6, Problem 6.14TYU

(a).

To determine

The small-signal transistor parameters gm,rπ,ro .

(a).

Expert Solution
Check Mark

Answer to Problem 6.14TYU

The values of small-signal parameters are,

  gm=7.73mAVrπ=15.5kΩ,ro=

Explanation of Solution

Given Information:

The circuit diagram is shown below.

  Microelectronics: Circuit Analysis and Design, Chapter 6, Problem 6.14TYU , additional homework tip  1

  β=120,VBE(on)=0.7V,VA=VCC=VEE=3.3V,RS=500Ω,RL=6,RB=100,RE=12,RC=12

Calculation:

The coupling and bypass capacitor act like open circuit for DC analysis. The AC voltage source ( vs ) is short circuited for DC analysis.

The modified figure is,

  Microelectronics: Circuit Analysis and Design, Chapter 6, Problem 6.14TYU , additional homework tip  2

Applying Kirchhoff’s voltage law in base-emitter loop,

  IBQRB+VBE(on)+IEQRE+VEE=0IBQRB+VBE(on)+(1+β)IBQRE+VEE=0IBQ=VEEVBE(on)RB+(1+β)REIBQ=(3.3)0.7100k+(1+120)12kIBQ=3.30.71552kIBQ=1.675μA

Determining the collector current,

  IBQ=1.675μAICQ=βIBQICQ=(120)(1.675μA)ICQ=0.201mA

Determining the Trans-conductance,

  gm=ICQVTgm=0.2010.026gm=7.73mAV

Determining the diffusion resistance rπ ,

  gmrπ=βrπ=βgmrπ=1207.73mAVrπ=15.5

Determining the small-signal transistor output resistance ro ,

  ro=VAICQro=0.201×103ro=

(b).

To determine

The small signal current gain (Ai=ioii) and small signal voltage gain (Av=vovs) .

(b).

Expert Solution
Check Mark

Answer to Problem 6.14TYU

The values of current and voltage gain,

  Ai=0.654Av=6.25

Explanation of Solution

Given Information:

The circuit diagram is shown below.

  Microelectronics: Circuit Analysis and Design, Chapter 6, Problem 6.14TYU , additional homework tip  3

  β=120,VBE(on)=0.7V,VA=VCC=VEE=3.3V,RS=500Ω,RL=6,RB=100,RE=12,RC=12

Calculation:

The coupling and bypass capacitors are short circuited for small-signal analysis. The DC voltage source is short circuited for small−signal analysis.

The modified figure is,

  Microelectronics: Circuit Analysis and Design, Chapter 6, Problem 6.14TYU , additional homework tip  4

Applying current division rule in output,

  Io=(RCRL+RC)(gmVπ)...(1)

Considering input circuit,

  Microelectronics: Circuit Analysis and Design, Chapter 6, Problem 6.14TYU , additional homework tip  5

  Vπ=Ib(rπ1+β)

Applying current division rule in input,

  Vπ=(rπ1+β)(RERE+rπ1+β)IiVπ=(rπ1+β||RE)Ii

From equation (1),

  Io=(RCRL+RC)(gm)((rπ1+β||RE)Ii)Ai=IoIi=gm(RCRL+RC)(rπ1+β||RE)=(7.73mAV)(12k12k+6k)(15.5k1+120||12k)=(5.153)(0.127)=0.654

Determining the small-signal voltage gain,

  Vo=(Rc||RL)(gmVπ)

Applying voltage division rule in input,

  Vπ=((RE||rπ1+β)Rs+(RE||rπ1+β))Vs

Plugging the value of Vπ ,

  Vo=(Rc||RL)(gm)(((RE||rπ1+β)Rs+(RE||rπ1+β))Vs)Av=VoVs=gm(Rc||RL)((RE||rπ1+β)Rs+(RE||rπ1+β))=(7.73mAV)(12k||6k)((12k||15.5k1+120)0.5k+(12k||15.5k1+120))=7.73×4×0.202=6.25

(c).

To determine

The values of input and output resistance.

(c).

Expert Solution
Check Mark

Answer to Problem 6.14TYU

The values of input and output resistance are,

  Ri=127ΩRo=12

Explanation of Solution

Given Information:

The circuit diagram is,

  Microelectronics: Circuit Analysis and Design, Chapter 6, Problem 6.14TYU , additional homework tip  6

  β=120,VBE(on)=0.7V,VA=VCC=VEE=3.3V,RS=500Ω,RL=6,RB=100,RE=12,RC=12

Calculation:

Considering the small signal equivalent circuit,

  Microelectronics: Circuit Analysis and Design, Chapter 6, Problem 6.14TYU , additional homework tip  7

The value of input resistance is,

  Microelectronics: Circuit Analysis and Design, Chapter 6, Problem 6.14TYU , additional homework tip  8

  Ri=RE||rπ1+β=12k||15.5k1+120=12k||0.128k=12×0.12812+0.128k=127Ω

Determining the output resistance,

  Ro=Rc=12

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Chapter 6 Solutions

Microelectronics: Circuit Analysis and Design

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