Lab-ReportAnalogue Electronics

The Common-Emitter Amplifier

Name: Dirk BeckerCourse: BEng 2Group: AStudent No.: 9801351Date: 30/10/1998

2

1. Contents

1. CONTENTS............................................................................................................................................22. INTRODUCTION .................................................................................................................................. 33. DC BIAS OF COMM ON-EMITTER AMPLIFIER ...........................................................................3

a) Measurment of the “ true” resistor values.................................................................................................. 3b) DC-bias precalculation with given resistors.............................................................................................4c) Measurement of DC-Voltages (DC-bias) ................................................................................................. 5d) Calculation of IB, IC and β with measured values.....................................................................................5

i. IB with IE and IC (RE and RC)................................................................ ................................ ..................... 5ii. IB with I1 and I2 (R1 and R2) ................................................................ ................................ ................. 5

4. AC AND SMALL SIGNAL CHARACTERISTICS............................................................................6a) BJT small signal behavioural model .........................................................................................................6b) Definitions of the small signal parameters................................................................................................6c) Measured small signal values...................................................................................................................7d) Calculation and derivation of the small signal parameters .......................................................................7

i. Amplifier input resistance Ri................................................................ ................................ ..................... 7ii. Amplifier output resistance Ro ................................................................ ................................ ............. 8iii. Voltage amplification without load Avo ................................................................ ................................ 9iv. Voltage amplification with load Av ................................................................ ................................ ...... 9v. Current amplification Ai ................................................................ ................................ .................... 10vi. Amplifier power gain Ap................................................................ ................................ ..................... 10

e) Comparison between measured and calculated values...........................................................................11i. DC-Bias ................................................................ ................................ ................................ .................. 11ii. Small signal parameters................................................................ ................................ ..................... 11

5. FREQUENCY RESPONSE OF THE CE-AMPLIFIER................................................................... 12a) Measured frequency response of Av .......................................................................................................12b) Determination of the theoretical cut-off f requency.................................................................................13c) Frequency response of A i........................................................................................................................16

6. DISCONNECTION OF BYPASS CAPACITOR C3 .........................................................................187. DC-BIAS WITH DISCONNECTED C3 .............................................................................................18

a) Calculation of DC-Bias...........................................................................................................................18b) Measurement of DC-Voltages (DC-bias) ...............................................................................................18c) Calculation of IB, IC and β with measured values( C3 disconnected)......................................................19

i. IB with IE and IC (RE and RC)................................................................ ................................ ................... 19ii. IB with I1 and I2 (R1 and R2) ................................................................ ................................ ............... 19

8. AC AND SMALL SIGNAL CHARACTERISTICS (WITHOUT C3) .............................................20a) BJT small signal behavioural model .......................................................................................................20b) Measured small signal values without C3 ...............................................................................................20c) Calculation and derivation of the small signal parameters (mid freq., without C3) ................................21

i. Amplifier input resistance Ri................................................................ ................................ ................... 21ii. Amplifier output resistance Ro ................................................................ ................................ ........... 22iii. Voltage amplification at mid frequencies without load................................................................ ...... 22iv. Voltage amplification at mid frequencies with load................................................................ ........... 23v. Current amplification Ai ................................................................ ................................ .................... 23vi. Amplifier power gain Ap................................................................ ................................ ..................... 24

d) Comparison between measured and calculated values...........................................................................249. FREQUENCY RESPONSE OF THE CE-AMPLIFIER WITHOUT C3.........................................25

a) Frequency response of Av .......................................................................................................................25b) Theoretical calculation of the lower cut-off frequency...........................................................................27c) Frequency response of A i without C3......................................................................................................29

3

2. Introduction

The common-emitter ampli fier is one of the most common discrete ampli fier used inconventional electronics. Its special characteristics were to be discovered in this lab session.

3. DC bias of common-emitter ampli fier

figure 1

a) Measurment of the “ true” resistor values

For calculating the correct bias values at first the real values of the used resistors andcapacitors have to be measured, because they all have got deviations from the printed values.

Also a measurement of the very small currents is not possible. So the voltage drop across thedifferent devices has to be determined and then the flowing current can be calculated via KCLand Ohm’s law.

The following values were measured:

RS=3.26kΩ C1=80.54µFR1=9.99kΩ C2=8.949µFR2=55.7kΩ C3=9.177µFRE=986ΩRC=3.82kΩRL=6.72kΩ

4

( )( )

V907.2V

V454.1V639.5V10V

VVVV

V454.1V

201A232.71000V

1I[RIRV

V639.5V

mA446.1k9.3V

IRV

mA446.1A232.7200II

A232.7k485.810001000200

V10k56k10

k10

RR

RRRR

VRR

R

RRR

VI

CE

CE

RERECCCE

RE

RE

BCEERE

RC

RC

CCRC

BC

21

21EE

CC21

1

IEE

OB

=−−=

−−=

=⋅µΩ=+β==

=⋅Ω=

=

=µ⋅=β=

µ=Ω+Ω+Ω⋅

Ω+ΩΩ

=

+++β

+=

++β=

b) DC-bias precalculation with given resistors β=200, VBE=0.7V

O1EEB

BIOBC

BIOEE

BE

CC21

1o

21

21I

V)RRR(IV0

IRV)II(V0

IRVRIV0

:KCL

V7.0Vwith

V515.1V10k56k10

k10V

RR

RV

k485.8k56k10

k56k10

RR

RRR

−++β=+−+=

+−=

=

=Ω+Ω

Ω=+

=

Ω=Ω+ΩΩ⋅Ω=

+=

! "

! "

#$ % & ' ( ) * + ( ,- .

- / 0 , - ! , 0 1 2 ,- 3

#$ 4 -

5 1 6 ,- 7 + 8 - 7 9 " :

V361.4V

V907.2V454.1VVV

mA140.0I

k56

V846.7

R

VI

V846.7V

V454.1V7.0V10V

VVVV

mA4536.1232.7201I

(I

C

CEREC

2R

2

2R2R

2R

2R

REBECC2R

E

E

=+=+=

=Ω

==

=−−=

−−=

=Αµ⋅=Ι1)+β= Β

mA215.0k10

V54.2

R

VI

1

1R1R =

Ω==

V154.2V846.7V10V

VVV

1R

2RCC1R

=−=−=

5

c) Measurement of DC-Voltages (DC-bias)

Next step was to measure the voltages in order to check the real bias and to calculate based onthis values the DC current ampli fication and the other occurring currents and voltages.

VR1=1.477V

VR2=8.51VVRE=0.863VVRC=3.33VVC=6.66VBE=0.618VCE=5.80

d) Calculation of IB, IC and ββ with measured values

i. IB with IE and IC (RE and RC)

ii . IB with I 1 and I2 (R1 and R2)

177A93.4

mA8713.0

I

I

93.4mA14785.0mA15278.0III

mA15278.0k7.55

V51.8

R

VI

mA14785.0k99.9

V477.1

R

VI

B

C

1R2RB

2

2R2R

1

1R1R

=µ

==β

Αµ=−=−=

=Ω

==

=Ω

==

235A7.3

mA8713.0

I

Ih

A7.3I

mA8713.0mA875.0I

III

mA8713.0k82.3

V33.3

R

VI

mA875.0986

V863.0

R

VI

B

Cfe

B

B

CEB

C

RCC

E

REE

=µ

===β

µ=−=

−=

=Ω

==

=Ω

==

6

4. AC and small signal characteristics

Next part of the lab was to determine the small signal characteristics of the common-emitterampli fier. Small signal characteristics are the essential values for the ampli fication function ofthe circuit.

For calculation of these characteristics a special model is used, the small signal model of theBJT. These models are derived from the characteristic curves of the real devices and, whenproperly devised, can be used to predict accurately the behaviour of semiconductor devices inpractical applications such as voltage and current ampli fication.

By computer simulation more complex models can be used.

a) BJT small signal behavioural model

; <; = <

; > ; ?

@ A @ ?@ B@ C

DE F GH I J

KJ L

H G M NL H O

G PL Q R S T U V S U W S X R H Y H Z

N K [L

figure 2

In the small signal model for mid frequencies the capacitors are short circuited because theirimpedance is negligble to the rest of the circuit.

b) Definitions of the small signal parameters

voc: open circuit output voltagevo: output voltage with loadvs: signal voltagevi: ampifier input voltagevrs: voltage drop across sensor resistorRi: ampli fier input resistanceRo: ampli fier output resistanceAvo: ampli fier voltage gain without loadAv: ampli fier voltage gain with loadA i: ampli fier current gainAp: ampli fier power gain

7

c) Measured small signal values(A generator with f=1kHz works as voltage source V1)

vs=20mVvoc=1.242Vvo=0.799Vvi=10.8mVvrs=9.1mV

d) Calculation and derivation of the small signal parameters

ALL THEORETICAL VALUES WITH INDEX ‘ (i.e. R’)

i. Ampli fier input resistance Ri

The theoretical value of Ri fits good with the determination due the measured values. Themeasurement of vi and i i was relative uncertain because of the small values and not using thewhole range of the measuring instrument (~20mV to 200mV Range).

\ ]\ ^ ]

\ _

` a` b

cd e fg h i

ji k

g l m n k g f f ok p q r s t u r

Ω=Ω

=== k87.3

k26.3mV1.9

mV8.10

rvv

i

vR

:R of valueMeasured

s

rs

i

i

ii

i

Ω=

Ω+

Ω+

Ω

=

ΩΩ=

=

==

==

k52.2

k578.31

k561

k101

1'R

mA453.1

mV26200||k56||k10'R

I

mV26h||R||R'R

I

mV26r with rh||R||R'R

h||R||Ri

v'R

:Rfor Values lTheoretica

i

i

Efe21i

Eeefe21i

ie21i

ii

i

figure 3

8

ii . Ampli fier output resistance Ro

v w x v w

y x

z | ~

|

figure 4

From these in the lab measured values hOE can be easily determined:

Ω=Ω

−Ω

=−

=

−=

+=

k1.142h

k82.3

1

k72.3

11

R

1

R

11

h

R

1

R

1

h

1

R

1

h

1

R

1

OE

CO

OE

COOE

COEO

It can be seen, that hOE can be let out at calculation of BJTs, because of its large value to therest of the circuit.

Ω=Ω

−=

−=

k72.3

k72.6V799.0

V799.0V242.1R

Rv

vvR

:R of valueMeasured

o

L

o

ooco

o

Ω===

k9.3'R

S0h withR'R

:R of valuelTheoretica

o

OECo

o

9

iii . Voltage ampli fication without load Avo

iv. Voltage ampli fication with load Av

218

mA4536.1mV26

k9.3'A

I

mV26h

Rh

h

Rh'A

ih

Rih

ih

Ri'A

v

v'A

:A of valueslTheoretica

vo

Efe

Cfe

ie

Cfevo

Bie

CBfe

Bie

Ccvo

Ri

ocvo

vo

L

=Ω=

−=−=

−=−

=

= ∞→

( )

( ) ( )

138

mA4536.1mV26

k479.2'A

ImV26

RR

RR

ImV26

RR'A

I

mV26h

RRh

h

RRh'A

ih

RRi'A

v

v'A

:A of valuelTheoretica

v

E

LC

LC

E

LCv

Efe

Lcfe

ie

Lcfev

Bie

LCcv

i

ov

v

=Ω=

+⋅

==

=−=

−=

=

115AmV8.10

V242.1A

v

vA

:A of valueMeasured

vo

vo

i

ocvo

vo

=

=

=

74AmV8.10

V799.0A

v

vA

:A of valueMeasured

v

v

i

ov

v

=

=

=

10

v. Current ampli fication A i

vi. Ampli fier power gain Ap

140'Ak485.8k58.3

k485.8200'A

RRImV26h

RRh

RRh

RRh'A

iRRh

RRiwith

i

ih'A

i

i'A

:A of valuelTheoretica

i

i

21E

fe

21fe

21ie

21fei

I21ie

21B

I

Bfei

I

Ci

i

=Ω+Ω

Ω=

+=

+=

+==

=

117Ak26.3

mV1.9k82.3

V242.1A

Rv

Rv

i

iA

:A of valueMeasured

i

i

s

rs

c

oc

I

Ci

i

=Ω

Ω=

==

( )

19494'AmA1436.1

mV26k479.2

k458.8k58.3

k458.8200'A

ImV26

RR

Rh

Rh'A

h

RRh

Rh

Rh'A

AA'A

:A of valuesTheeoretic

p

p

E

LC

Iie

Ifep

ie

LCfe

Iie

Ifep

vip

p

=

Ω⋅Ω+Ω

Ω=

+=

+=

⋅=

8658'A

11774'A

AA'A

:A of valueMeasured

p

p

vip

p

=

⋅=

⋅=

11

e) Compar ison between measured and calculated values

i. DC-Bias

Measurand VRC VRE VCE VC VR1 VR2 hfe

measured 3.33V 0.863V 5.80V 6.66V 2.154V 7.846V 237/177

calculated 5.639V 1.454V 2.907V 4.361V 2.154V 7.846V 200

ii . Small signal parameters

Measurand Rin Rout Avo Av A i Ap

measured 3.87 kΩ 3.72kΩ 115 74 117 8685calculated 2.52 kΩ 3.9kΩ 218 138 140 19494

The measured and the calculated values are partly very different. Major problem of thedetermination of the Bias and the small signal parameters were the uncertain measurements.Especially the small values like IB and the input current of the small signal equivalent circuitwere very diff icult to determine exactly.

12

5. Frequency response of the CE-amplifier

a) Measured frequency response of Av

The voltage ampli fication over a range from 10Hz to 1kHz was to measure to determine thecut-off frequency of the CE-Ampli fier.

f/Hz 10 20 50 70 100 120 200 500 700 1000vi/mV 13.1 12.8 11.4 11.1 10.7 11.4 10.2 10 10 10vo/mV 183.4 0.324 555 618 667 730 714 734 736 738vo/vi 14 25.31 48.7 55.7 62.3 64 70 73.4 73.6 73.8

The cut-off frequency is defined as the frequency, when the ampli fication is dropped down to70.7% (-3dB or ½√2).Below this frequency there is still ampli fication, but the frequency range of ampli fiers iscommonly defined by the 3dB cut-off freuency.

Voltage Amplification vs frequency

10

100

10 100 1000f

Av

maxvA2

1dB3 =−

figure 5

fc=58Hz

13

b) Determination of the theoretical cut-off f requency

¡ ¢ £ ¤ ¥ ¥

figure 6

Figure 6 shows the equivalent circuit for low and mid frequencies.To determine the cut-off frequency the input and output circuit has to be separated.

figure 7

¦ §¦ ¨ ¦ ©¦ ª

« ¬ ­« ®« ¬ ®

« ©¯ °± ² ³¯ ±± ² ³

´ ¯µ ¶ · ¸ ¹ º ·± »¼ ½

¼ °¾ ¿ » ¼ ±± ² » ¿ À Á »¼  à ± ¼ ¯Ä À Å »Æ Ç È É Æ Ç Ê Ë Ì« ¨

The cut-off frequency of the CE-Ampli fier is above all depending on the emitter bypasscapacitor CE=C3. The impedance of the two coupling capacitors is about 1500Ω at 10Hz eachand can be neglected because of these small values in comparison to the rest of the circuit.

For the input circuit:

1

Cj

R)1(

1Cj

R

11

1)Z( Zwhere

ZRh

vI

E

E

EE

EEIn

EInInie

iB

+βω+

+β

1=ω+

+β=+β=

++=

Input OutputCurrent sourceÍ ic=constant

14

The current through (β+1)RE can be neglected because of it’s large resistance

EInie

inB

C

1jRh

vi

ω+β−+

=

The current IB will drop to 70.7% of it’s maximum value when the voltage drop at (hie+RIn)and ZE are of the same magnitude.

Hz54f2

f

s

1337

)k577.3k38.2(F100

201

k38.2RRRR where)hR(C

1

hR

1

C1

cc

c

S21inieinE

cutoff

ieInE

=π

ω=

=Ω+Ωµ

=ω

Ω==+

+β=ω

+=

+βω

The calculated cut-off f requency is with 54Hz very close at the measured value of 58 Hz.The exact calculation of the cut-off frequency is very complex and is done in most cases witha computer and a simulation software like (P) or (H)spice.On the following pages (P)spice printouts of the simulated CE-Ampli fier can be found.

Î Ï Ï ÐÑ Ò

Î Ï ÐÑ Î Î Ï ÐÑ Ó

Ò Ô Õ Ö× Ñ

Ø Ó Ù Ó Ó Ó ÓØ Î

Î Ö× Ú× Î Î Ï ÖÒ Ô Ò Ö× ÛÜÝ Þ Û

ß à Ö× Ó

× á à Ô â ÖÜÝÎ Ó Þ Þ ÎÎ Ô ã à Ï Þ

ã Ô à â à ÞÎ Ô Î Î Ò Þ

Î Ô Î Ï à ä å

à Ô Õ Î æ Ð å

Î Ô Î Î Ò ä å

Î â Ó Ô â ã Ð å

figure 8

figure 8 shows the BIAS calculated by a (P)spice simulation.

15

Spice printout of frequency response AV

16

c) Frequency response of A i

f/Hz 10 20 50 70 100 120 200 500 700 1000vrs/mV 4.5 6.2 8.0 8.3 8.7 8.9 9.1 9.2 9.2 9.3vo/mV 197 351 600 668 720 738 771 792 795 797

AR

v

s

rs µ1.38 1.90 2.45 2.54 2.67 2.73 2.79 2.82 2.82 2.85

AR

v

L

o µ29.31 52.23 89.29 99.4 107 110 115 118 118 119

A i 21 27.5 36 39 40 40,5 41 42 42 42

The cut-off frequency of the current ampli fication is read out from the diagram 23Hz.This frequency is above all determined by the capacitor CE.

Current Amplification vs frequency

10

100

10 100 1000f

Ai

maxiA2

1dB3 =−

fc=23Hz

figure 9

17

Spice printout of the frequency response of the current ampli fication A i vs frequency

18

6. Disconnection of bypass capacitor C3

Next step of the Lab was to disconnect the Emitter bypass capacitor to proof the importanceof the bypass capacitor especially on the voltage and current ampli fication, the main

çè é

ç

ê é ë ìì éí î í í í íé ë ï é ë ïè íð ñ ð òó ô

õ ö òó í ð ñ ÷ òó è

é òó øó éé ë ò ó ùö ñ ú òê ì ôfigure 10

Figure 10 shows the schematics of the CE-Ampli fier with disconnected C3.

7. DC-Bias with disconnected C3

a) Calculation of DC-Bias

The calculated DC-Bias with disconnected capacitor C3 can’ t change, because C3 has noinfluence to any DC-values. C3 is not used for calculation of the DC-Bias and so it’s not ableto change it.û

see DC-Bias values at DC-bias precalculation with given resistors

b) Measurement of DC-Voltages (DC-bias)

The same DC-bias measurements were to make with disconnected C3 li ke in the first part ofthe Lab.

VR1=1.479V

VR2=8.47VVRE=0.849VVRC=3.27VVC=6.65VBE=0.625VCE=5.81

19

c) Calculation of IB, IC and ββ with measured values( C3 disconnected)

i. IB with IE and IC (RE and RC)

ii . IB with I 1 and I2 (R1 and R2)

213A01.4

mA856.0

I

I

01.4mA14805.0mA15206.0III

mA15206.0k7.55

V47.8

R

VI

mA14805.0k99.9

V479.1

R

VI

B

C

1R2RB

2

2R2R

1

1R1R

=µ

==β

Αµ=−=−=

=Ω

==

=Ω

==

The different values of β=hfe can be led back to the uncertainty of measurement, because themeasured values were very small and at the lower range of the measuring instrument.

2.171A5

mA856.0

I

Ih

A5I

mA856.0mA861.0I

III

mA856.0k82.3

V27.3

R

VI

mA861.0986

V849.0

R

VI

B

Cfe

B

B

CEB

C

RCC

E

REE

=µ

===β

µ=−=

−=

=Ω

==

=Ω

==

20

8. AC and small signal characteristics (without C3)

Next part of the lab was to determine the small signal characteristics of the common-emitterampli fier.

By computer simulation more complex models can be used.

a) BJT small signal behavioural model

With the disconnected Capacitor C3 another model of the circuit has to be used now, becausethe Emitter Resistor is now not short circuited at mid-frequencies and generates an importantcurrent feedback of the AC-signals through IE, which reduces the ampli fication of the CE-Ampli fier considerably.

ü ýü þ ü ÿü

ü

ÿ

figure 11

All the definitions can be taken from Definitions of the small signal parameters

b) Measured small signal values without C3

The input voltages are increased by a factor 10 to obtain better measurands at the low

ampli fications without bypass capacitor.(A generator with f=1kHz works as voltage source V1)

vs=200mVvoc=533mVvo=340mVvi=143mVvrs=57.3mV

21

c) Calculation and derivation of the small signal parameters (mid freq., without C3)

ALL THEORETICAL VALUES WITH INDEX ‘ (i.e. R’)

i. Ampli fier input resistance Ri

TheFigure 12 shows, that the Emitter resistor is divided into two parts for separating input andoutput circuit.The connection between both is given through the voltage drop at the emitter resistor RE.

The calculated value of Rin is very close to the measured value. The approximation of REin canbe done because there’s a negligible difference between hfe and (hfe+1).

[ ]

Ω≈Ω×+Ω

+Ω

+Ω

≈

+≈

++=

+==+=

k15.8'Rk1200k577.3

1

k10

1

k56

11

'R

)Rhh(RR'R

R)1h(hRR'R

i

iR)1h(

i

vR where)Rh(RR'R

:R of valuelTheoretica

in

in

Efeie12in

Efeie12in

B

BEfe

B

REEInEInie12in

in

! " # $

% & '% (% & (

% #

) *+ , -) ++ , - ./ 0 )1 2 3 4 5 6 3+ 78 9

8 *: ; 7 8 ++ , 7 ; < = 78 >./ ? + 8 )@ < A 78 B 6 C 8 B D - E

Ω=Ω

=

==

k14.8Rk26.3

mV3.57mV143

R

Rv

v

i

vR

:R of Value Measured

in

in

s

rs

i

i

iin

in

figure 12

22

ii . Ampli fier output resistance Ro

F G H F G

I H

JK L MN O P Q

L R

figure 13

It’s the same small signal model than in the first part. The series connection of the currentsource and the emitter resistor can be reduced to the current source only.

The calculated and the measured value are again very close together.

iii . Voltage ampli fication at mid frequencies without load

83.3k1200k577.3

k9.3200A

Rhh

Rh

R)1h(h

RhA

)Rh(

RhA

)Rh(i

Rih

v

v'A

:A of valuelTheoretica

vo

Efeie

Cfe

Efeie

Cfevo

Einie

Cfevo

EinieB

CBfe

i

ocvo

vo

=Ω⋅+Ω

Ω⋅=

+≈

++−=

+−

=

+−

==

The Voltage ampli fication is very low, because the emitter resistor without bypass capacitorcauses a current feedback which results in a low Ampli fication at all frequencies (seefrequency response).

Ω=Ω

−=

−=

k81.3

k72.6mV340

mV340mV533R

Rv

vvR

:R of valueMeasured

o

L

o

ooco

o

Ω===

k9.3'R

S0h withR'R

:R of valuelTheoretica

o

OECo

o

3.3amV143

mV533A

v

vA

:A of valueMeasured

vo

vo

i

ocvo

vo

=

=

=

23

iv. Voltage ampli fication at mid frequencies with load

45.2k1200k577.3k8.6k9.3

k8.6k9.3200

'A

Rhh

)RR(h

R)1h(h

)RR(h'A

)Rh(

)RR(h'A

)Rh(i

)RR(ih

v

v'A

:A of valuelTheoretica

v

Efeie

LCfe

Efeie

LCfev

Einie

LCfev

EinieB

LCBfe

i

ov

vo

=Ω⋅+ΩΩ+ΩΩ⋅Ω⋅

=

+≈

++−=

+−

=

+−

==

The ampli fication without bypass capacitor is again very low, but the theoretical value and themeasured value are very close together.

v. Current ampli fication A i

38.2AmV143

mV340A

v

vA

:A of valueMeasured

vo

vo

i

ocvo

vo

=

=

=

8'A

k485.8)201(k1k58.3

k485.8200'A

RR)1h(RImV26h

RRh

RR)1h(Rh

RRh'A

iRRR)1h(h

RRiwith

i

ih'A

i

i'A

:A of valuelTheoretica

i

i

21feEE

fe

21fe

21feEie

21fei

I21Efeie

21B

I

Bfei

I

Ci

i

≈Ω+Ω+Ω

Ω=

+++=

+++=

+++==

=

93.7Ak26.3

mV3.57k82.3

mV533A

Rv

Rv

i

iA

:A of valueMeasured

i

i

s

rs

c

oc

I

Ci

i

=Ω

Ω=

==

24

vi. Ampli fier power gain Ap

d) Compar ison between measured and calculated values

Measurand hfe Rin Rout Avo Av A i Ap

measured 171/213

8.14kΩ 3.81kΩ 3.3 2.38 8 19

calculated 200 8.15kΩ 3.9kΩ 3.83 2.45 8 19

19'A

k1200k577.3

k479.2

k48.8201k1k577.3

k48.8200'A

Rhh

RR

RR)1(Rh

RRh'A

AA'A

:A of valuesTheeoretic

p

p

Efe

ie

LC

21Eie

21fep

vip

p

=

Ω+ΩΩ×

Ω+⋅Ω+ΩΩ=

+×

++β+=

⋅=

19'A

38.293.7'A

AA'A

:A of valueMeasured

p

p

vip

p

=

⋅=

⋅=

25

9. Frequency response of the CE-amplifier without C3

a) Frequency response of Av

f/Hz 10 20 50 70 100 200 500 700 1000vi/mV 134 131.8 131.4 131.2 131.3 130.9 130.9 730.9 130.9vo/mV 305 309 311 310 311 310 310 310 310vo/vi 2.3 2.3 2.4 2.3 2.3 2.3 2.3 2.3 2.3

fc is notreadable

and so the cut-off frequency is much lower than 10Hz. The current ampli fication is linear overthe low and mid frequency band.

Voltage Amplification vs frequency

1

10

10 100 1000f

Av

figure 14

26

(P)spice printout of the Voltage Ampli fication without bypass capacitor

27

b) Theoretical calculation of the lower cut-off f requency

At this circuit only the coupling capacitors have an influence to the lower cut -off fr equencybecause the bypass capacitor is removed.

S TS U S VS W

X Y ZX [X Y [

X V

\ ]^ _ `\ ^^ _ ` ab c \d e f g h i f^ j

k lk ]m n j k ^^ _ j n o p jk qa

b r ^ k \s o t jk u ^ jX U

figure 15

figure 15 shows the small signal equivalent circuit for the CE-Ampfli fier with disconnectedbypass capacitor.

S TS U S VS W

X Y ZX [X Y [

X V

\ ]^ _ `\ ^^ _ ` ab c \d e f g h i f^ j

k lk ]m n j k ^^ _ j n o p jk qa

b r ^ k \s o t jv w x y v w z |X U

figure 16

In figure 16 the emitter resistor is separated into its input and output circuit part.

For the input circuit:

)Rh(RR wherev

CRj

11)Rh(

1i

Cj

1R

v

RhR

Ri

RhRR

RRi

Cj

1R

vi

EinieBini

1inEinie

B

1in

i

EinieB

Bi

Einie21

21B

in

ii

+=

ω

++=

ω+++

=++

=

ω+

=

28

For the output circuit:

B

2CL

feLCo

LC

LCLCb

2CL

feCLoLo

Bfe

2LC

Cc

2LC

Co

i

C)RR(j

11

h)RR(v

RR

RRRR wherei

Cj

1RR

hRRiRv

ih

Cj

1RR

Ri

Cj

1RR

Ri

+ω+

=

+=

ω++

−=−=

ω++

=

ω++

=

Combining the I /P and O/P circuit

[ ]

)s1)(s1(

sA

v

v)s(A

C)RR(

C)R)h1(h(RCR

R)h1(h

)RR(hA where

)Rh(CRj

11

1

C)RR(j

11

h)RR(

v

vA

21

221

vmidi

oV

2LC2

1EfeieB1In1

Efeie

LCfevmid

Einie1In2CL

feLC

i

ov

τ+τ+ττ

==

+=τ++==τ

++−=

+ω

++ω

+−==

Using the calculated values:

Hz2

55.1

)s(

s

A

)s(A

Hz48.12

fHz34.91

s107.0

F10)k8.6k9,3(

Hz95.12

f28.121

s081.0

F10)k14.8k48.8(

c

CL

2c

2

2

2c

2

mid21

21c

22

2

2

11c

11

1

1

≈ωω=ω

ω+ωω=

ω+=⇒ω≈ω

=π

ω=⇒=

τ=ω

=τµΩ+Ω=τ

=π

ω=⇒=τ

=ω

=τµΩΩ=τ

This low frequency was not measurable in the lab, because the generator and the measuringinstruments were not able to determine such a low frequency correctly.The ampli fication of the CE-Ampli fier without bypass capacitor reaches nearly into the DC-region.

29

figure 17

c) Frequency response of A i without C3

f/Hz 10 20 50 70 100 200 500 700 1000vrs/mV 56 57 57 57 57 57 57 57 57vo/mV 333 337 339 339 340 339 339 339 339

AR

v

s

rs µ17.17 17.5 17.5 17.5 17.5 17.5 17.5 17.5 17.5

AR

v

L

o µ49.55 50 50.5 50.5 50.5 50.5 50.5 50.5 50.5

A i 2.88 2.87 2.88 2.88 2.88 2.88 2.88 2.88 2.88

fc is not readable and so the cut-off frequency is much lower than 10Hz.

The current and voltage ampli fication of the CE-ampli fier is very low, but constant during thelower frequencies, therefor the CE-Ampli fier without bypass capacitor is not often used.For low frequency ampli fication usually direct coupled ampli fiers with bypass capacitors areused. If the circuit is well designed the lower cut-off frequency is mostly determined by theemitter capacitor and NOT by the coupling capacitors.

Current Amplification vs frequency

1

10

10 100 1000f

Ai

30

(P)spice printout of the current ampli fication vs frequency