ELEC3509_Lab2

ELEC 3509 LAB 2

AMPLIFIER PROJECT

Authors:Dean SHEPHERDSON

Zachary DUNNIGAN

Student Number:100829563100892725

Submitted: Friday November 7, 2014

Amplifier Project - Dean Shepherdson 100829563, Zach Dunnigan 100892725 - Final Copy 1

Contents1 Introduction 3

2 Transistor Amplifier Characterization 32.1 Small Signal Parameter Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.1 Common Emitter Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1.2 Common Collector Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.3 Common Base Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1.4 Common Emitter - Common Base Amplifier . . . . . . . . . . . . . . . . . . . . 142.1.5 Common Collector - Common Base Amplifier . . . . . . . . . . . . . . . . . . . 192.1.6 Common Collector - Common Emitter Amplifier . . . . . . . . . . . . . . . . . . 25

3 Single Transistor and Two-Transistor Amplifiers 303.1 Circuit Construction and DC Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 303.2 AC Measurements for Single-Transistor Amplifiers . . . . . . . . . . . . . . . . . . . . . 31

3.2.1 Common Emitter Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2.2 Common Collector Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.2.3 Common Base Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3 AC Measurements for Two Transistor Amplifiers . . . . . . . . . . . . . . . . . . . . . . 353.3.1 Common Emitter - Common Base Amplifier . . . . . . . . . . . . . . . . . . . . 353.3.2 Common Collector - Common Base Amplifier . . . . . . . . . . . . . . . . . . . 363.3.3 Common Collector - Common Emitter Amplifier . . . . . . . . . . . . . . . . . . 37

3.4 Link Between Single and Two Stage Amplifiers . . . . . . . . . . . . . . . . . . . . . . . 38

4 Cascode Specification and Design 404.1 Design Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.1.1 DC Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.1.2 AC Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.2 DC Biasing Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.3 Cascode Gain Specification Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.4 Cascode Frequency Specification Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5 Cascode Implementation and Verification 48

6 Conclusion 53


1 IntroductionThe purpose of this lab was to investigate a variety of amplifiers which used BJT transistors as circuitelements. Three basic single BJT amplifiers which consisted of the CE, CC, and CB configuration wereconstructed and had their DC and AC characteristics measured and recorded as well as their input and out-put impedance’s. Following this, combinations of the three basic configurations were connected to formmore complex amplifiers with two BJT transistors. The CE-CB, CC-CB, and the CC-CE configurationwere investigated to observe performance improvements in both gain and bandwidth. Similar AC charac-teristics were measured and recorded for each new combined amplifier as well as their input and outputimpedance’s as was done before.

A specific configuration of the CE-CB amplifier known as a Cascode amplifier was then designed tomeet specific performance requirements including its gain, high frequency pole, and low frequency polefor a pre-determined load resistance. This design was constructed, tested, and modified accordingly inthe lab to meet these design specifications. A comparison between the performance of the constructedconfiguration of the Cascode amplifier in the lab and the initial design of the the Cascode amplifier wasthen performed. Discrepancies between the pre-calculated parameters and the measured values from thefinal circuit are then explained in detail.

This report will outline single and two stage amplifiers and their DC and AC parameters. It will alsooutline the design and implementation of a cascode amplifier.

2 Transistor Amplifier CharacterizationIn this section, the theoretical parameters for each amplifier including input and output impedance’s, midband gain, high and low frequency poles were characterized using the ideal resistor and capacitor values.

NOTE: Equivalent Input Resistance Network

For the following instances where RS is indicated - it is referred to as an equivalent resistance to thenetwork shown below in figure 1.

Figure 1: Source Resistance Network [1]

This network is needed since the minimum output amplitude of the of the signal generator is not lowenough. Node x is then connected to the respective input branch of each amplifier.Since this was performed before taking any measurements β was assumed to be 150.


2.1 Small Signal Parameter CalculationsThis segment will overview the theoretical calculations based on the small signal analysis of each ampli-fier.The DC biasing conditions were provided, with the given component values shown in figure 2.

Figure 2: Nominal Component Values [1]

2.1.1 Common Emitter Amplifier

Figure 3: Common Emitter Amplifier [Dean]

Figure 3 represents the Device Under Test (DUT) for this segment. The corresponding small signalmodel extracted from the above configuration can be seen in figure 4.

Figure 4: Common Emitter Small Signal Model [Dean]

The following small signal parameters were then calculated using the above small signal model.


Input Impedance:

Rin = R12||R22||rπ +R3

Rin = 6.6kΩ

Output Impedance:

Rout = RC2

Rout = 5.6kΩ

Gain:

Av =vπvs

vovπ

vπvs

=

(R12||R22||rπ

R12||R22||rπ +RS

)vovπ

= −gm(RC2||RL)

∴ Av = −(

R12||R22||rπR12||R22||rπ +RS

)(gm(RC2||RL))

Av = 50.49V

V

High Frequency Cut-off:Figure 5 shows the high frequency circuit for the common emitter amplifier.

Figure 5: CE High Frequency Circuit [Dean]

The left side high frequency pole is represented in figure 6:

Figure 6: High Frequency Circuit: Pole 1 [Dean]

C1 = Cµ (1 + gm(RC2||RL)) , C2 = Cµ

(1 +

1

gm(RC2||RL)

)Amplifier Project - Dean Shepherdson 100829563, Zach Dunnigan 100892725 - Final Copy 5

Req = RS||R12||R22||rπCeq = Cπ + C1

Ceq = Cπ + Cµ (1 + gm(RC2||RL))

Therefore the first high frequency pole is given by:

ωh1 =1

ReqCeq=

1

(RS||R12||R22||rπ) · [Cπ + Cµ (1 + gm(RC2||RL))]= 7.28× 105 rad

s

The right side high frequency pole is represented in figure 7

Figure 7: High Frequency Circuit: Pole 2 [Dean]

Req = RC2||RL

Ceq = C2 = Cµ

(1 +

1

gm(RC2||RL)

)Therefore the second high frequency pole is given by:

ωh2 =1

ReqCeq=

1

(RC2||RL) · Cµ(

1 + 1gm(RC2||RL)

) = 1.73× 109 rad

s

The overall high frequency cut-off can be found by:

fh =

(ωh1ωh2

ωh1 + ωh2)

)· 1

2π= 115.7kHz

Low Frequency Cut-offCin:

Figure 8: Low Frequency Circuit: Pole 1 [Dean]

ωL1 =1

(RS +Rin) · Cin= 15

rad

s




Cout:

ωL2 =1

(Rout +RL) · Cout= 44.3

rad

s

CE:

ωL3 =1

(RS+Rin(1+β)

)||RE2 · CE= 229.8

rad

s

Therefore the overall low frequency cut-off can be found by:

fL = (ωL1 + ωL2 + ωL3)1

2π= 60.5Hz

2.1.2 Common Collector Amplifier

Figure 11: Common Collector Amplifier [Dean]

Figure 11 represents the DUT for this segment. The corresponding small signal model extracted fromthe above configuration can be seen in figure 12.


Figure 12: Common Collector Small Signal Model [Dean]

The following small signal parameters were then calculated using the above small signal model.Input Impedance:

Rin = R11||R21||(rπ + (1 + β)(RE1||RL)) +R3

Rin = 28.9kΩ

Output Impedance:

Rout = RE3||(rπ +R11||R21||RS)

1 + β

Rout = 44.7Ω

Gain:

Av =vπvs

vovπ

vπvs

=

(Rin

Rin +RS

)vovπ

=

((RE1||RL)(1 + β)

(RE1||RL)(1 + β) + rπ

)∴ Av =

(Rin

Rin +RS

)((RE1||RL)(1 + β)

(RE1||RL)(1 + β) + rπ

)Av = 0.873

V

V

High Frequency Cut-off:The high frequency circuit diagram in figure 13 can be written equivalently as shown in figure 14.

Req = (rπ + β(RE1||RL))||RS||R11||R21

Ceq = Cµ +Cπ

1 + gm(RE1||RL)

Therefore the high frequency cut-off is given by:

ωh1 =1

ReqCeq=

1

((rπ + β(RE1||RL))||RS||R11||R21)(Cµ + Cπ

1+gm(RE1||RL)

) = 7.28× 105 rad

s


Figure 13: CC High Frequency Circuit (1) [Dean]

Figure 14: CC High Frequency Circuit (2) [Dean]

Since there is only one high frequency cut off, it can be written in terms of Hertz as:

fh = (ωh1) ·1

2π= 115.8kHz

Low Frequency Cut-off

Figure 15: CC Low Frequency Circuit: Pole 1 [Dean]

Req = (RS||R11||R21||(rπ + (RE1||RL)(1 + β)))

Ceq = Cin

Cin:

ωL1 =1

ReqCeq=

1

(R11||R21||(rπ + (RE1||RL)(1 + β))) · Cin= 3.9

rad

s

Req = (rπ +RS||R11||R21

1 + β)||RE1 +RL)

Ceq = Cout


Figure 16: CC Low Frequency Circuit: Pole 2 [Dean]

Cout:

ωL2 =1

ReqCeq=

1

( rπ+RS ||R11||R21

1+β)||RE1 +RL) · Cout

= 96.8rad

s


fL = (ωL1 + ωL2)1

2π= 16.0Hz

2.1.3 Common Base Amplifier

Figure 17: Common Base Amplifier [Dean]


Figure 18: Common Base Small Signal Model [Dean]



Rin = RE3||reRin = 3.32kΩ

Output Impedance:

Rout = RC

Rout = 5.6kΩ

Gain:

Av =vπvs

vovπ

vπvs

= −(

RE3||re3(RE3||re3) +RS

)vovπ

= − (gm(RC ||RL))

∴ Av =

(RE3||re3

(RE3||re3) +RS

)(gm(RC ||RL))

Av = 0.757V

V

High Frequency Cut-off:

Figure 19: CB High Frequency Circuit [Dean]

Using the left side of figure 19 to determine the first high frequency pole:

Req = (RE3||re||RS)

Ceq = Cπ

ωh1 =1

ReqCeq=

1

(RE3||re||RS) · Cπ= 74.4× 106 rad

s

Using the right side of 19 to find the second high frequency pole:

Req = (Rout||RL)

Ceq = Cµ

ωh2 =1

ReqCeq=

1

(Rout||RL) · Cµ= 97.84× 106 rad

s


fh =

(ωh1ωh2

ωh1 + ωh2)

)· 1

2π= 6.72MHz


Low Frequency Cut-offFigure 20 was used to determine the first low frequency pole.

Figure 20: CB Low Frequency Circuit: Pole 1 [Dean]

Req = (RS +Rin)

Ceq = Cin

Cin:

ωL1 =1

(RS +Rin) · Cin= 29.6

rad

s

Figure 21 was used to determine the second low frequency pole.


Req = (Rout +RL)

Ceq = Cout

Cout:

ωL2 =1

(Rout +RL) · Cout= 44.3

rad

s


Figure 22 was used to determine the third low frequency pole.


Req = (R13||R23||(rπ + (1 + β)RE3)

Ceq = CB

CB:

ωL3 =1

(R13||R23||(rπ + (1 + β)RE3) · CB= 17.1

rad

s


fL = (ωL1 + ωL2 + ωL3)1

2π= 14.5Hz


2.1.4 Common Emitter - Common Base Amplifier

Figure 23: CE-CB Amplifier [Dean]


Figure 24: CE-CB Small Signal Model [Dean]


Rin = R12||R22||rπ +R3

Rin = 6.60kΩ

Output Impedance:

Rout = RC3

Rout = 5.6kΩ

Gain:

Av =vπ1vs

vπ2vπ1

vovπ

vπvs

=

(R12||R22||rπ

R12||R22||rπ +RS

)vπ2vπ1

= (gm(RC2||RE3||re2))vovπ

= (−gm(RC3||RL))

∴ Av = −(

R12||R22||rπR12||R22||rπ +RS

)(gm(RC2||RE3||re2)) (gm(RC3||RL))

Av = −50.18V

V


High Frequency Cut-off:Figure 25 represents the high frequency CECB circuit.

Figure 25: CECB High Frequency Circuit [Dean]

Figure 26 was used to determine the first high frequency pole. Notice, capacitor C1 is derived from millers

Figure 26: CECB High Frequency Circuit: Pole 1 [Dean]

theorem on Cµ.

C1 = Cµ(1 + gm(RC1||RE3))

Req = RS||R12||R22||rπCeq = Cπ1 + Cµ(1 + gm(RC1||RE3))

ωh1 =1

ReqCeq=

1

[RS||R12||R22||rπ] · [Cπ1 + Cµ(1 + gm(RC1||RE3))]= 1.74× 106 rad

s

Figure 27 was used to determine the second high frequency pole. C2 is the other half of the miller theorem



effect.

C2 = Cµ[1 +1

gm(RC1||RE3

]

Req = RC1||RE3||re

Ceq = Cπ2 + Cµ[1 +1

gm(RC1||RE3

]

ωh2 =1

ReqCeq=

1

(RC1||RE3||re) · (Cπ2 + Cµ[1 + 1gm(RC1||RE3)

])= 3.36× 109 rad

s

Figure 28 was used to determine the second high frequency pole.


Req = RC3||RL

Ceq = Cµ2

ωh3 =1

ReqCeq=

1

(RC3||RL) · (Cµ2)= 9.84× 107 rad

s


fh =

(1

ωh1+

1

ωh2+

1

ωh3

)−1· 1

2π= 272.4kHz

Low Frequency Cut-offFigure 29 represents the CECB low frequency circuit.

Figure 29: CECB Low Frequency Circuit [Dean]


Figure 30 was used to determine the first low frequency pole.

Figure 30: CECB Low Frequency Circuit: Pole 1 [Dean]

Req = RS +R12||R22||rπCeq = Cin

Cin:

ωL1 =1

ReqCeq=

1

(RS +R12||R22||rπ) · (Cin)= 15

rad

s



Req = RC3 +RL

Ceq = Cout

Cout:

ωL2 =1

ReqCeq=

1

(RC3 +RL) · (Cout)= 44.1

rad

s




Req = RE2||[RS||R12||R22||rπ

β + 1

]Ceq = CE

CE:

ωL3 =1

ReqCeq=

1

(RE2||[RS ||R12||R22||rπ

β+1

]) · (CE)

= 910rad

s

Figure 33 was used to determine the fourth low frequency pole.


Req = RC1 +RE3||reCeq = Ccouple

Ccouple:

ωL4 =1

ReqCeq=

1

(RC1 +RE3||re) · (Ccouple)= 1.78

rad

s


Figure 34 was used to determine the fifth low frequency pole.


Req = R13||R23|| [(β + 1)(RC2||RE3 + re)]

Ceq = CB

CB:

ωL5 =1

ReqCeq=

1

(R13||R23|| [(β + 1)(RC2||RE3 + re)]) · (CB)= 17.63

rad

s


fL = (ωL1 + ωL2 + ωL3 + ωL4 + ωL5)1

2π= 157.3Hz

2.1.5 Common Collector - Common Base Amplifier

Figure 35: CC-CB Amplifier [Dean]

Figure 35 represents the DUT for this segment.


The corresponding small signal model extracted from the above configuration can be seen in figure 36.

Figure 36: CC-CB Small Signal Model [Dean]


Rin = R11||R21|| [rπ1 + (β + 1)(RE1||RE3||re2)] +R3

Rin = 9.20kΩ

Output Impedance:

Rout = RC3

Rout = 5.6kΩ

Gain:

Av =vπ2vs

vovπ2

−vπ2vs

=

[(RE1||RE3||re2)(β + 1)

[rπ1 + (RE1||RE3||re2)(β + 1)] ||R21||R11 +RS

]vovπ2

= (−gm(RC3||RL))

∴ Av =

[(RE1||RE3||re2)(β + 1)

[rπ1 + (RE1||RE3||re2)(β + 1)] ||R21||R11 +RS

](gm(RC3||RL))

Av = 41.1V

V


High Frequency Cut-off:

Figure 37 represents the CCCB high frequency circuit.

Figure 37: CCCB High Frequency Circuit [Dean]

Figure 38 was used to determine the first high frequency pole.

Figure 38: CCCB High Frequency Circuit: Pole 1 [Dean]

Req = (RS||R11||R21)|| [rπ1 + β(RE1||RE3||re2)]

Ceq = Cµ1 +Cπ1

1 + gm(RE1||RE3||re2)

Ceq1:

ωh1 =1

ReqCeq=

1

(RS||R11||R21)|| [rπ1 + β(RE1||RE3||re2)] ·[Cµ1 + Cπ1

1+gm(RE1||RE3||re2)

] = 5.85×107 rad

s




Req = (RE1||RE3||re2)||[RS||R11||R21 + rπ1

β + 1

]Ceq = Cπ2

Cπ2:

ωh2 =1

ReqCeq=

1

(RE1||RE3||re2)||[RS ||R11||R21+rπ1

β+1

]· Cπ2

= 7.87× 109 rad

s

Figure 40 was used to determine the third high frequency pole.


Req = RC3||RL

Ceq = Cµ2

Cµ2 :

ωh3 =1

ReqCeq=

1

RC3||RL · Cµ2= 9.78× 107 rad

s

Therefore the overall high frequency for the CCCB amplifier can be found by:

fh =

(1

ωh1+

1

ωh2+

1

ωh3

)−1· 1

2π= 5.80Mhz




Figure 41: CCCB Low Frequency Circuit: Pole 1 [Dean]

Req = RS + [R11||R12||(rπ1 + (β + 1)(RE1||RE3||re3))]Ceq = Cin

Cin:

ωL1 =1

ReqCeq=

1

RS + [R11||R12||(rπ1 + (β + 1)(RE1||RE3||re3))] · (Cin)= 10.8

rad

s



Req = RC3 +RL

Ceq = Cout

Cout:

ωL2 =1

ReqCeq=

1

RC3 +RL · (Cout)= 44.1

rad

s




Req = R13||R23||[rpi3 + (RE3||RE1)(β + 1)]

Ceq = CB

CB:

ωL3 =1

ReqCeq=

1

R13||R23||[rpi3 + (RE3||RE1)(β + 1)] · (CB)= 18.0

rad

s



Req = (RE3||re3) + [RE1||(rπ1 +RS||R11||R21

β + 1

)]

Ceq = Ccouple

Ccouple:

ωL4 =1

ReqCeq=

1

(RE3||re3) + [RE1||(rπ1+RS ||R11||R21

β+1

)] · (Ccouple)

= 677.91rad

s


fL = (ωL1 + ωL2 + ωL3 + ωL4)1

2π= 119.35Hz


2.1.6 Common Collector - Common Emitter Amplifier

Figure 45: CC-CE Amplifier [Dean]


Figure 46: CC-CE Small Signal Model [Dean]


Rin = R11||R21||[rπ1 + (β + 1)(RE1||R12||R22||rπ2)] +R3

Rin = 29.71kΩ

Output Impedance:

Rout = RC2

Rout = 5.6kΩ


Gain:

Av =vπ2vs

vovπ2

vπ2vs

=(β + 1)(rπ2||RE1||R12||R22)

R12||R11|| [(β + 1)(rπ2||RE1||R12||R22) + rπ1] +RS

vovπ2

= −gm(RC2||RL)

∴ Av = −[

(β + 1)(rπ2||RE1||R12||R22)

R12||R11|| [(β + 1)(rπ2||RE1||R12||R22) + rπ1] +RS

](gm(RC2||RL))

Av = −34.38V

V

High Frequency Cut-off:Figure 47 was used to determine the first high frequency pole.

Figure 47: CCCE High Frequency Circuit: Pole 1 [Dean]

Req = (RS||R11||R21)||[rπ1 + β(RE1||R12||R22||rπ2)]

Ceq = Cµ1 +Cπ1

1 + gm(RE1||R12||R22||rπ2)

Ceq1:

ωh1 =1

ReqCeq=

1

[(RS||R11||R21)||[rπ1 + β(RE1||R12||R22||rπ2)]] · [Cµ1 + Cπ21+gm(RE1||R12||R22||rπ2) ]

= 8.21×107 rad

s


C1 = Cµ2[1 + gm(RC2||RL)]

Req = (RE1||R21||R22||rπ2)||(rπ1||RS||R11||R12

β + 1

)Ceq = Cπ2 + C1

Ceq2:

ωh2 =1

ReqCeq=

1

(RE1||R21||R22||rπ2)||(rπ1||RS ||R11||R12

β+1

)· [Cπ2 + Cµ2[1 + gm(RC2||RL)]]

= 2.17×108 rad

s





C2 = Cµ2[1 +1

1 + gm(RC2||RL)]

Req = RC2||RL

Ceq = C2

Ceq3:

ωh3 =1

ReqCeq=

1

[RC2||RL] · [Cµ2[1 + 11+gm(RC2||RL)

]]= 9.69× 107 rad

s

Therefore the overall high frequency for the CCCE amplifier can be found by:

fh =

(1

ωh1+

1

ωh2+

1

ωh3

)−1· 1

2π= 5.87Mhz



Req = R11||R12||[rπ1 + (1 + β)(RRE1||R12||R22||rπ2] +RS

Ceq = Cin

Cin:

ωL1 =1

ReqCeq=

1

[(R11||R12||[rπ1 + (1 + β)(RRE1||R12||R22||rπ2] +RS] · (Cin)= 3.96

rad

s


Figure 50: CCCE Low Frequency Circuit: Pole 1 [Dean]



Req = RC2 +RL

Ceq = Cout

Cout:

ωL2 =1

ReqCeq=

1

(RC2 +RL) · (Cout)= 44.1

rad

s


Req = RE2||

(rπ2 +R12||R22||RE1)||(rπ1+(RS ||R11||R21

1+β

)1 + β

Ceq = CE

CE:

ωL3 =1

ReqCeq=

1

(RE2||[(rπ2+R12||R22||RE1)||

(rπ1+(RS ||R11||R21

1+β

)1+β

]) · (CE)

= 228rad

s





Req = (R12||R22||rπ2) +

(RS||R11||R21 + rπ1

1 + β||RE1

)Ceq = Ccouple

Ccouple:

ωL4 =1

ReqCeq=

1[(R12||R22||rπ2) +

(RS ||R11||R21+rπ1

1+β

)||RE1

]· (Ccouple)

= 9.04rad

s


fL = (ωL1 + ωL2 + ωL3 + ωL4)1

2π= 45.37Hz


3 Single Transistor and Two-Transistor AmplifiersIn this section, three separate single transistor amplifier configurations and three combinations of twotransistor amplifiers were constructed and built to specific DC biasing constraints. The results help showthe strengths and weaknesses of each amplifier.

3.1 Circuit Construction and DC MeasurementsThe circuits shown in figure 54 represent the layout for each single transistor amplifier.

Figure 54: Circuit Configurations of Single Transistor Amplifiers [1]

For each transistor, the relevant DC measurements taken can be found in table 1.

Table 1: DC Measurements

CC: Voltages (V) Resistors kΩ Current (mA)VCC 15.09 R1,1 98.5 IC 1.03VB 4.08 R2,1 38.6 IE 1.04VE 3.42 RC1 5.61 IB 0.0061VC 9.3 RE1 3.28

CE: Voltages (V) Resistors kΩ Current (mA)VCC 15.09 R1,2 98.6 IC 1.01VB 4.01 R2,2 38.6 IE 1.01VE 3.34 RC2 5.66 IB 0.0085Vc 9.38 RE2 3.3

CB: Voltages (V) Resistors kΩ Current (mA)VCC 15.09 R1,3 98.5 IC 1.04VB 4.09 R2,3 38.8 IE 1.04VE 3.44 RC3 5.57 IB 0.0062VC 9.3 RE3 3.31


By quick inspection the voltage difference between the collector and the emitter in each transistor is suf-ficiently large enough to say that they are in active mode. Another important piece of information is thecurrent in the collector. They are all within %10 of our desired 1mA collector current bias. With thesebiasing conditions we can conclude that we can proceed to the AC analysis with each transistor performingas intended.

RC1 can be made to zero when testing the common collector amplifier because considering the smallsignal analysis shown in section 2.1.2, it has no effect on any of the small signal parameters including:input/output resistances or gain. It is required in the determining the DC operating point to ensure thecollector current is set to approximately 1mA and also to help measure VCE . Once VCE is found suchthat the transistor is in active mode - removing RC1 will only force the device farther into active mode byincreasing VCE .

Alternatively you could use a bypass capacitor - considering the AC analysis, it gives the same resultas replacing RC1 with a short circuit.

Capacitors CE2 and CB are required for the AC characteristics of the amplifier. In the case of CE2 - itwill bypass the degeneration resistor RE2 CC amwhich is desired. This degeneration resistor would causea large reduction of gain which is not always wanted. It’s purpose is only for the DC biasing of the circuit.As for the CB capacitor, it’s purpose is to eliminate the high input impedance that would otherwise becaused by R13 and R23. Ideally a low input impedance typically ≈ 50Ω is required for a common baseamplifier. These nodes cannot simply be shorted to ground or VCC since this would cause a large shift inthe DC bias point.

3.2 AC Measurements for Single-Transistor AmplifiersComments on Differences:

Small variations between calculated and measured values expected as for 4 possible reasons:

• The actual R/C values measured in the lab differed from their theoretical values used in calculationfor all amplifiers.

• Beta values were assumed to be 150 but in reality can vary.

• Measured values are only as good as the accuracy of the measurement, small errors in measurementscan have large influences on the parameters determined from them.

• All measured values for Rout are expected to be low since ro and rµ were neglected in theoreticalanalysis. The parallel combinations would cause the calculated values to drop by a small amount

NOTE: When a measured value only differs from its corresponding calculated value by a small amount,the deviation is attributed to one of the three reasons listed above. Otherwise an additional explanationwill be included.


3.2.1 Common Emitter Amplifier

Table 2 represents the data taken for the gain parameters of the CE amplifier. Rin: Calculated: 6.6kΩ -

Table 2: Gain Measurements: CE Amplifier

Frequency (Hz) Voltages (mV pk-pk) Resistances kΩ Gain VV

1006 vout 2000 Rin 4.457419 Amid 47.61905vU 42 Rout 5.115 dB 33.55561vT 11

vU − vT 31v′out 4200

Measured: 4.4kΩ. The measuredRin was very dependent on the vT measurement. If vT was measuredeven a few mV off, the change in measured Rin is large.Rout : Calculated: 5.6kΩ - Measured: 5.11kΩ. This measurement was deemed within acceptable range.Amid : Calculated: 50.49 - Measured: 47.62. This measurement was deemed within acceptable range.

Table 3 represents the data taken for the high and low frequency cutoff’s of the CE amplifier.

Table 3: Frequency Cutoff Measurements: CE Amplifier

High Frequency CutoffVoltages (mV pk-pk) fH (Hz)vout 1400 181807vU 42

Low Frequency CutoffVoltages (mV pk-pk) fL (Hz)vout 1400 41vU 42

fH : Calculated: 115.7kHz - Measured: 181.8kHz. This measurement was extremely dependent onthe values of Cπ and Cµ, the calculated fH used values from a data sheet for Cπ and Cµ but those valueswere for a very specific IC and frequency. Cπ andCµ were likely different than the actual values used incalculation from the data sheet. Small changes in the capacitance values have a large influence on thispole. Additionally, it is possible the accuracy of oscilloscope when determining the 3dB drop was notperfect.fL: Calculated: 60.6Hz - Measured: 41Hz. This measurement had an acceptable order of magnitude. Thedifference is likely due to the accuracy of the oscilloscope when determining the 3dB drop.

The CE amplifier had a high gain, a moderate input and output impedance, and a low bandwidth. Theseproperties are due to the nature of the input into the base and the output in the collector. The input andoutput impedance’s are both moderate in this configuration.. The low bandwidth is due to the miller effect


which causes an increase in input capacitance which effectively reduces the high frequency pole of theamplifier. These properties make the CE amplifier a good voltage amplifier.

3.2.2 Common Collector Amplifier

Table 4 represents the data taken for the gain parameters of the CC amplifier.

Table 4: Gain Measurements: CC Amplifier

Frequency (Hz) Voltages (mV pk-pk) Resistances kΩ Gain (V/V)1017 vout 2000 Rin 32.0775 Amid 0.854701

vU 2340 Rout 0.093 dB -1.36372vT 2100

vU − vT 240v′out 2040

Rin: Calculated: 28.9kΩ - Measured: 32.08kΩK. This measurement was deemed within acceptablerange.Rout : Calculated: 0.045kΩ - Measured: 0.093kΩ. This measurement was very dependent on the value ofbeta due to reflection through the emitter. The value of beta was assumed to be 150, if it was different itwould change the value of Rout correspondingly.Amid : Calculated: 0.873 - Measured: 0.855. This measurement was deemed within acceptable range.

Table 5 represents the data taken for the high and low frequency cutoff’s of the CC amplifier.

Table 5: Frequency Cutoff Measurements: CC Amplifier

High Frequency CutoffVoltages (mV pk-pk) fH (Hz)vout 1400 2.914 MvU 2340


fH : Calculated: 13.21MHz - Measured: 2.914MHz. This measurement was extremely dependent onthe values of Cπ and Cµ, the calculated fH used values from a data sheet for Cπ and Cµ but those valueswere for a very specific IC and frequency. Cπ andCµ were likely different than the actual values used incalculation from the data sheet. Small changes in the capacitance values have a large influence on thispole. Additionally, it is possible the accuracy of oscilloscope when determining the 3dB drop was notperfect.fL: Calculated: 16Hz - Measured: 14Hz. This measurement was deemed within acceptable range.


The CC amplifier had a gain which is less than unity - a large input impedance - a small output impedanceand a large bandwidth. These properties are due to the configuration of the input into the base and theoutput out of the emitter. The CC amplifier’s approximately unity voltage gain and large bandwidth makeit a good voltage buffer.

3.2.3 Common Base Amplifier

Table 6 represents the data taken for the gain parameters of the CB amplifier.

Table 6: Gain Measurements: CB Amplifier


vU 2520 Rout 5.3 dB -2.007vT 32

vU − vT 2488v′out 4280

Rin: Calculated: 3.32kΩ - Measured: 3.33kΩK. This measurement was deemed within acceptablerange.Rout : Calculated: 5.6kΩ - Measured: 5.3kΩ. This measurement was deemed within acceptable range.Amid : Calculated: 0.757 - Measured: 0.793. This measurement was deemed within acceptable range.

Table 7 represents the data taken for the high and low frequency cutoff’s of the CB amplifier.

Table 7: Frequency Cutoff Measurements: CB Amplifier



fH : Calculated: 6.727MHz - Measured: 3.33MHz. This measurement was extremely dependent on thevalues of Cπ and Cµ, the calculated fH used values from a data sheet for Cπ and Cµ but those values werefor a very specific IC and frequency. Cπ andCµ were likely different than the actual values used in cal-culation from the data sheet. Small changes in the capacitance values have a large influence on this pole.Additionally, it is possible the accuracy of oscilloscope when determining the 3dB drop was not perfect.fL: Calculated: 14.5Hz - Measured: 12Hz. This measurement was deemed within acceptable range.


The CB amplifier had a gain less than unity (due to degeneration resistor), a moderate input impedance(due to degeneration resistor), and a moderate output impedance. The bandwidth of this amplifier is largedue to the high frequency pole not suffering from miller effect; the base connecting to ground allows Cπand Cmu to be isolated. This amplifier without the degeneration resistor R3 would have an appreciablegain and also a small input impedance and moderate output impedance and could be used as a voltageamplifier. With the inclusion of the degeneration resistor this circuit could be used as a voltage buffer asthe gain can be controlled down to approximately unity.

3.3 AC Measurements for Two Transistor Amplifiers3.3.1 Common Emitter - Common Base Amplifier

Table 8 represents the data taken for the gain parameters of the CECB amplifier.

Table 8: Gain Measurements: CECB Amplifier


vU 39.6 Rout 4.65 dB 34.07vT 21.2

vU − vT 18.4v′out 4000

Rin: Calculated: 6.6kΩ - Measured: 7.08kΩK. This measurement was deemed within acceptablerange.Rout : Calculated: 5.6kΩ - Measured: 4.65kΩ. This measurement was deemed within acceptable range.Amid : Calculated: 50.18 - Measured: 50.5. This measurement was deemed within acceptable range.

Table 9 represents the data taken for the high and low frequency cutoff’s of the CECB amplifier.

Table 9: Frequency Cutoff Measurements: CECB Amplifier

High Frequency CutoffVoltages (mV pk-pk) fH (Hz)vout 1400 3.24 MvU 39.6

Low Frequency CutoffVoltages (mV pk-pk) fL (Hz)vout 1400 42vU 39.6

fH : Calculated: 272KHz - Measured: 324KHz. This measurement was extremely dependent on thevalues of Cπ and Cµ, the calculated fH used values from a data sheet for Cπ and Cµ but those values werefor a very specific IC and frequency. Cπ andCµ were likely different than the actual values used in cal-culation from the data sheet. Small changes in the capacitance values have a large influence on this pole.


Additionally, it is possible the accuracy of oscilloscope when determining the 3dB drop was not perfect.fL: Calculated: 157.3Hz - Measured: 42Hz. In the low frequency pole pre-calculation for this amplifier,the dominant capacitor that had the largest effect on the low frequency pole was CE . CE’s equivalentresistance had a large dependence on beta due to reflection from the base to emitter. Any variance in thevalue of beta had a large effect on the equivalent resistance for the CE capacitor and consequently the totallow frequency pole.

The performance improvements when the CE and CB amplifiers were connected to form a CE-CB am-plifier consisted of a high gain from the CE amp and a large bandwidth from the CB amp. The inputimpedance was moderate for the same reasons as in the CE amp; the input of this amplifier was throughthe CE . The output impedance was also moderate for the same reasons as in the CB amp. The output ofthis amplifier was connected to the collector of the CB portion. The CE-CB amplifier is good for voltageamplification over a larger range of frequencies when compared to the single CE amplifier.

3.3.2 Common Collector - Common Base Amplifier

Table 10 represents the data taken for the gain parameters of the CCCB amplifier. Rin: Calculated: 9.2kΩ

Table 10: Gain Measurements: CCCB Amplifier


vU 69.2 Rout 3.72 dB 29.22vT 52.4

vU − vT 16.8v′out 3600

- Measured: 13.5kΩK. vU was likely measured high - decreasing vU produces an Rin closer to the ex-pected value. This also corrects the error in gain which is positive reinforcement that this is likely a badmeasurement.Rout : Calculated: 5.6kΩ - Measured: 3.72kΩ. The variation could be due to v′out being measured too lowwhich would reduce the measured value of Rout.Amid : Calculated: 41.1 - Measured: 28.9. This measurement was low for the same reason as the Rin.

Table 11 represents the data taken for the high and low frequency cutoff’s of the CCCB amplifier.fH : Calculated: 5.8MHz - Measured: ¿4.11MHz. This measurement was deemed acceptable - the

generator would not go to high enough frequency to create the 3dB drop.fL: Calculated: 119Hz - Measured: 316Hz. In the low frequency pole pre-calculation for this amplifier,the dominant capacitor was Ccouple. Ccouple’s equivalent resistance had a large dependence on beta due toreflection from the base to emitter. Any variance in the value of beta had a large effect on the equivalentresistance for the Ccouple capacitor and consequently the total low frequency pole.

Connecting the CC and CB amplifiers together produced a CC-CB amplifier with a large gain but notas large as the CE-CB due to the additional resistance reflected to the base of the CC amp from the emit-ters connection to the CB amp. The input impedance compared to the single CC amp was reduced due toan additional parallel reflected resistance from the emitter’s connection to the CB. The output impedance


Table 11: Frequency Cutoff Measurements: CCCB Amplifier



was relatively the same compared to the CB as the only resistor determining it was RC. The bandwidth ofthis amplifier is larger than both the CC or CB which both had a large bandwidth to begin with.

3.3.3 Common Collector - Common Emitter Amplifier

Table 12 represents the data taken for the gain parameters of the CCCE amplifier.

Table 12: Gain Measurements: CCCE Amplifier


vU 54.8 Rout 5.21 dB 31.24vT 49.4

vU − vT 5.4v′out 4240

Rin: Calculated: 29.7kΩ - Measured: 33.4kΩK. This measurement was deemed to be within an ac-ceptable range.Rout : Calculated: 5.6kΩ - Measured: 5.2kΩ. This measurement was deemed to be within an acceptablerange.Amid : Calculated: 34.4 - Measured: 36.5. This measurement was deemed to be within an acceptablerange..

Table 13 represents the data taken for the high and low frequency cutoff’s of the CCCE amplifier.fH : Calculated: 5.87MHz - Measured: 2.0MHz. This measurement was extremely dependent on

the values of Cπ and Cµ, the calculated fH used values from a data sheet for Cπ and Cµ but those valueswere for a very specific IC and frequency. Cπ andCµ were likely different than the actual values used incalculation from the data sheet. Additionally, the equivalent resistances for two out of the three equivalentcapacitance’s which were used to calculate the total high frequency pole were largely dependent on thevalue of beta. Variations in beta would cause changes in the calculated expected high frequency polefL: Calculated: 45Hz - Measured: 65Hz. This measurement had an acceptable order of magnitude. Thedifference is likely due to the accuracy of the oscilloscope when determining the 3dB drop.


Table 13: Frequency Cutoff Measurements: CCCE Amplifier

High Frequency CutoffVoltages (mV pk-pk) fH (Hz)vout 1400 2.00 MvU 54.8


Connecting the CC and CE amplifiers together produced a CC-CE amplifier with a gain larger than theCC-CB amp but smaller than the CE-CB amp. The gain calculation is similar to what occurred in theCC-CB amp however the second stage of the amplifier was connected to the base of a CE instead of theemitter of a CB. Consequently the reflected resistance as seen through the base of the first CC transistorstage was larger because of a reflected parallel combination with rπ instead of with the much smaller resis-tance re as was seen in the CC-CB. The input impedance was large and similar to that of the CC amplifierdespite the reflected resistance from the base of the CE amplifier. This is because the reflected resistancefrom the base of the CE was very large and when put in parallel with the input resistors of the CC thereflected resistance essentially had no effect. The output impedance remained the same as seen in the CEamp which was RC. The bandwidth of this amplifier is much larger than the single CE amplifier due to theCC stage which shifted the overall high frequency pole much higher.

3.4 Link Between Single and Two Stage AmplifiersIn the first part of this lab, single transistor amplifiers of the CE, CC and CB configuration were investi-gated. Each amplifier had its input impedance, output impedance, gain, and bandwidth explored and andperformance summarized. The performance advantages of each amplifier varied with their configurations.

The CE amp was found to have large gain, moderate input impedance, moderate output impedance, anda small bandwidth. The CC amp was found to have gain less than unity, large input impedance, smalloutput impedance, and a large bandwidth. The CB amp was found to have gain less than unity due tothe degeneration resistor (otherwise would be larger than unity), a moderate input impedance again due tothe degeneration resistor (otherwise would be small), moderate output impedance, and a large bandwidth.Each amplifier had their own advantages and disadvantages which is the reason the two stage amplifierswere explored next.

By combining each of the single stage amplifiers into two stage amplifiers in the cascade configuration,performance improvements were accomplished which combined the advantages of both amplifiers in eachtwo stage combination. The CE-CB amp was able to maintain a large gain with moderate input and outputimpedance but the bandwidth was increased when compared to a single CE amp. The CC-CB amp wasable to achieve a gain greater than unity with moderate input and output impedances and possessed aneven larger bandwidth than the individual CC or CB amps. The CC-CE amp achieved a large gain withthe large input impedance of the CC yet the moderate output impedance of the CE; its bandwidth was alsolarge due to the high frequency poles created by the CC stage of the amp.


The purpose of this process was to demonstrate that various desired performances can be achieved fordifferent tasks through combining amplifiers in two stages. Additionally, this paved the way for the nextsection of this lab which will investigate a specific configuration of the CE-CB amplifier known as theCascode amplifier.

4 Cascode Specification and DesignThis section will outline the necessary requirements for the cascode amplifier design, as well as the actualdesign process.

4.1 Design RequirementsThe following requirements for the cascode amplifier design were determined by the process outlined inthe lab manual.

Some of the values are functions of a value produced by a series of calculations on each partners stu-dent number. The following value denoted Z is found by the sum of the last 3 digits of the combinedstudent numbers:

Z = 100829563 + 100892725 = 201722288,∴ 2 + 8 + 8 = 18

The required load resistance was found to be:

RL = 5(Z + 51)2 = 23.8kΩ,∴ 27kΩ

The value was rounded up to the nearest value actually possible in the lab.The magnitude of the gain was determined by:

|AV | = (Z3

40− 1.03Z2 + 11Z + 12)± 5% = 22.08± 5%

4.1.1 DC Specifications

No DC current may flow in to RL and also may not flow into or out of the signal generator. Collectorcurrents in the transistors are to be 1.0mA ± 10%. Power supply voltages are limited to +15V andground. Lastly, the total circuit power consumption must be less than 50mW .

4.1.2 AC Specifications

The high frequency cut-off must exceed 600kHz, while the low frequency cut-off must appear in the rangebetween 60 − 200Hz. The output voltage should be able to reach 2Vpk−pk without appreciable distortion- jagged edges, clipping, fuzziness of signal. AC base-emitter voltage must be kept under 10mVpk−pk forthe 2Vpk−pk output. Input and output impedance’s are left to the discretion of the designers.

All other components are the designers choice - with no adjustable components allowed.


4.2 DC Biasing DesignThis subsection will cover the steps taken throughout the DC biasing design phase.Figure 55 represents the DC biasing circuit used to begin the design process using the constraints listedabove.

Figure 55: Cascode Amplifier DC Biasing Circuit [Dean]

Reasonable assumptions and recommendations:

• Current in Ix is 10x the sum of the two base currents ∴ Ix = 10(IB1 + IB2)

• Choose VEC = 3V for max output swing

• β = 150

• Choose largest voltage drop across RC possible, accounting for VCE’s and small drop across RE

• VBE = 0.7V

With the given restraints and helpful starting points, the DC design could now be completed.

It was recommended that a small drop be sustained across the resistor RE . This is desired since wewish to keep the largest amount of voltage to drop across RC . The voltages were back calculated usingthe fact that IC = 1mA. RC was chosen to be 8.2kΩ since this would mean the voltage at VC2 would haveto be 8.2V in order to have the collector current set to 1mA. Then, choosing a VEC = 3V to allow for themaximum output swing we determined the voltages at VC1 = 11.2V and then the voltage at VE1 = 14.2to allow for some room to adjust the resistor RE which is actually two smaller resistors in series as far asthe DC biasing is concerned. Later the analysis will show that in AC one of the series resistors will bebypassed by a capacitor in the AC operation of the amplifier. We found this configuration to be acceptablesince we know both transistors will be in active mode and behave as expected if the outlined voltages canbe obtained.

Therefore, since the voltages along the right branch have been defined - we can use this to determine


the base voltages of each transistor, which in turn will allow the values for the resistors in the left sidebranch to be calculated. Using the property that VEB = 0.7V the voltage on the base of transistor 1 can befound by:

VB1 = VE1 − VEB = 14.2V − 0.7V = 13.5V

Similarly, the voltage at VB2 can be found by:

VB2 = [VE1 − VCE]− VEB = [14.2V − 3V ]− 0.7V = 10.5V

In order to finally calculate the resistor values for R1, R2 and R3 we need to determine the current in thebranch. If the current Ix is taken to be large compared to IB the contribution to the current flowing fromthe base’s of each transistor can be neglected.

Using IC = 1mA we find the current in the base of both transistors to be:

IB = IB1 = IB2 =ICβ

=1mA

150= 6.66µA

Therefore, we set the current in the left side branch to be roughly 20x the base current or 10x the sum ofboth base currents:

Ix = 20IB ≈ 0.133mA,∴ Ix = 0.15mA

Now that the current Ix is known, the values for the resistors along that branch can be determined.

R1 =VCC − VB1

Ix=

15V − 13.5V

0.15mA= 10kΩ

R2 =VB1 − VB2

Ix=

13.5V = 10.5V

0.15mA= 20kΩ

R3 =VB2 − 0

Ix=

10.5

0.15mA= 69.3kΩ

Table 14 shows all the key elements of the DC biasing calculations.

Table 14: DC Design Specification Summary

Node Voltage (V) Resistors (kΩ) CurrentsVE1 14.2 R1 10 IC 1mAVC1 11.2 R2 20 IB 6.66µAVC2 8.2 R3 69.3 Ix 0.15mAVB1 13.5 RE 0.8VB2 10.5 RC 8.2


4.3 Cascode Gain Specification DesignFigure 56 represents the small signal model for the cascode amplifier.

Figure 56: Cascode Small Signal Model [Dean]


Rin = R4 +R1||R2||[rπ1 + (β + 1)RE2]

Rin = 6.94kΩ

Output Impedance:

Rout = RC

Rout = 8.2kΩ

Gain:

Av =vπ1vs

vπ2vπ1

vovπ2

vπ1vs

=

(rπ1

rπ1 +RS +R4 +RE2(1 + β)

)vπ2vπ1

= (gmre) = α

vovπ2

= (−gm(RC ||RL))

∴ Av = −α(

rπ1rπ1 +RS +R4 +RE2(1 + β)

)(gm(RC ||RL))

The gain required was found to be |Av| = 22.08VV

, calculated in section 4.1. Given that:

• rπ = βgm

= 3.75kΩ

• gm(RL||RC) = 251.6

• gmre ≈ 1

The gain expression can be evaluated as:

|Av| = 22.08 =

[3.75kΩ

3.8kΩ +R4 + 151RE2

]251.6

→R4 + 151RE2 = 38.93kΩ


The resistors R4 and RE2 play a large roll in reducing the gain produced by the amplifier as seen in theequation above. If RE2 is taken to be 250Ω, this would result in R4 = 1.2kΩ. Substituting these valuesinto the equation above yields:

|Av| =[

3.75kΩ

3.8kΩ + 1.2kΩ + 151(250Ω)

]251.6 = 22.07

This value is almost exactly the gain required from section 4.1. If the resistor RE2 = 250Ω then the resultof the series combination of the two degeneration resistors would be:

RE1 +RE2 = 800Ω,∴ RE1 = 800−RE2 = 550Ω

Raising RE2 but a small amount greatly reduces the gain - on the other hand if R4 is increased it may stillproduce the correct gain with a small RE2, however it will be shown that R4 has a large impact on the highfrequency cutoff of the circuit. This had to be kept in mind when varying these values.

4.4 Cascode Frequency Specification DesignThis section will outline the process used to design the high and low frequency cutoff points for the cas-code amplifier.

High Frequency Cut-offFigure 57 shows the high frequency circuit for the common emitter amplifier. The values for Cπ and Cµwere taken from the datasheet for the 2N3906 transistors as 10pF and 4.5pF respectively for the high fre-quency calculations.

Figure 57: Cascode High Frequency Circuit [Dean]

Figure 58 was used to determine the first high frequency pole.

Figure 58: Cascode High Frequency Circuit: Pole 1 [Dean]


C1 = Cµ (1 + gmre)

Req = R1||R2||(RS +R4)||(rpi + βRE2)

Ceq = Cµ (1 + gmre) +Cπ

1 + gmRE2

Therefore the first high frequency pole is given by:

ωh1 =1

ReqCeq=

1

(R1||R2||(RS +R4)||(rpi + βRE2)) ·[Cµ (1 + gmre) + Cπ

1+gmRE2

] = 9.80× 107 rad

s



C2 = Cµ

(1 +

1

gmre

)

Req = re

Ceq = C2 + Cπ2

Therefore the second high frequency pole is given by:

ωh2 =1

ReqCeq=

1

(re) ·[(

1 + 1gmre

)+ Cπ2

] = 2.11× 109 rad

s



Req = RC ||RL

Ceq = Cµ


Therefore the third high frequency pole is given by:

ωh3 =1

ReqCeq=

1

(RC ||RL) · [Cµ]= 3.53× 107 rad

s

Therefore the overall high frequency cut-off was found to be:

fH =

[1

ωh1+

1

ωh2+

1

ωh3

]−11

2π= 4.08MHz (1)

Low Frequency Cut-offFigure 61 shows the low frequency circuit for the cascode amplifier.

Figure 61: Cascode Low Frequency Circuit [Dean]


Figure 62: Cascode Low Frequency Circuit: Pole 1 [Dean]

Req = RS +R4 + [R1||R2||(rπ1 + (β + 1)RE2)]

Ceq = Cin

ωL1 =1

ReqCeq=

1

[RS +R4 + [R1||R2||(rπ1 + (β + 1)RE2)]] · (Cin)




Req = RC +RL

Ceq = Cout

ωL2 =1

ReqCeq=

1

[RC +RL] · (Cout)



Req = RE1||[RE2 + (β + 1)rπ1 + (β + 1)(R1||R2||(RS +R4)]

Ceq = CE

ωL3 =1

ReqCeq=

1

[RE1||[RE2 + (β + 1)rπ1 + (β + 1)(R1||R2||(RS +R4)]] · (CE)




Req = R3||[R2 +R1||(RS +R4)||[rπ1 + (β + 1)RE2]

Ceq = CB

ωL4 =1

ReqCeq=

1

[R3||[R2 +R1||(RS +R4)||[rπ1 + (β + 1)RE2]] · (CB)

Since once capacitor will dominate the low frequency cutoff - if three of the capacitors are chosen arbi-trarily - the remaining capacitor can be solved such that it produces the desired low frequency cut off. Thedesign chosen required a low frequency cut off of 120Hz. Therefore, to find the dominant capacitor thefollowing expression was used - assuming Cout = CE = CB = 2.2µF :

Cin = [2π(120Hz)− ωL2 − ωL3 − ωL4] ·Reqin = 0.2µF

This requires a very low value for Cin. By choosing the values of three arbitrarily we are limited to asingle value of Cin to produce the desired low frequency cutoff. Essentially placing the weight of the lowfrequency pole on one capacitor. This is most likely not the best design choice. By varying each valuefor each capacitor individually - it would increase the weight each pole had on the overall low frequencycutoff. This means that better capacitor values could be chosen instead of arbitrarily fixing them. Thiswould require many iterations and is easiest to perform in the lab.

5 Cascode Implementation and VerificationThis section will cover the actual values used in the amplifier as well as the extracted data.Table 15 represents the actual values of each resistor used in the circuit.

Table 15: Resistor Values: Cascode Amplifier

R Values kΩR1 11.341R2 13.31R3 74.44RC 8.11RE1 0.675RE2 0.217RL 26.8R4 0.578Rs1 0.469Rs2 0.0551


Table 16 represents the actual capacitor values used in the circuit.

Table 16: Capacitor Values: Cascode Amplifier

C Values (uF)Cin 10

Cout 3.3CE 4.7CB 0.1

Table 17 represents the data taken for the gain parameters of the CECB Cascode amplifier.

Table 17: Gain Measurements: CECB Cascode Amplifier


vU 91 Rout 7.77 dB 26.84vT 82

vU − vT 9v′out 2580

Rin: Calculated: 6.94kΩ - Measured: 5.84kΩK. The actual values for the resistors used in the lab weresmaller than theoretically planned. Therefore the slight reduction in actual values would account for thelower Rin measured. R4 was approximately half of the theoretical value - the series contribution from R4

would reduce Rin directly by the difference in these two values. The larger contribution however was thesmaller RE2 since this term was being multiplied by the (β + 1) factor, a small reduction of RE2 wouldresult in a smaller calculated Rin.

Rout : Calculated: 8.2kΩ - Measured: 7.77kΩ. This measurement was deemed to be within an acceptablerange. The most likely reason the measured value was low - was due to a measurement error. Although,in reality RC is in parallel with rµ which is assumed to be infinity - but practically is not. Therefore, thiscombination would slightly reduce Rout.

Amid : Calculated: 22.08 - Measured: 21.98. This measurement was deemed to be within an accept-able range of ±5% This was the purpose of the lab.


Table 18 represents the data taken for the high and low frequency cutoff’s of the CECB Cascodeamplifier.

Table 18: Frequency Cutoff Measurements: CECB Cascode Amplifier

High Frequency CutoffVoltages (mV pk-pk) fH (Hz)vout 1400 955.3kvU 91


fH : Calculated: 4.08MHz - Measured: 955.3kHz. This measurement was extremely dependent onthe values of Cπ and Cµ, the calculated fH used values from a data sheet for Cπ and Cµ but those valueswere for a very specific IC and frequency. Cπ andCµ were likely different than the actual values usedin calculation from the data sheet. Some of the difference can be accounted by smaller resistor valuesactually being used in the lab.

fL: Calculated: 120Hz - Measured: 164Hz. This measurement had an acceptable order of magnitude.The difference was largely attributed to using different capacitor values in the lab. The pre-calculationswere a rough estimate of what values to choose. The best option determined in the lab was found by trial.Table 19 represents the verification data such that the AC vbe remained under 10mV for both the CE andCB stages of the amplifier.

Table 19: AC vbe Verification

Tansistor: CE (mV pk-pk)vbe 9.6

Tansistor: CE (mV pk -pk)vbe 8.4

As seen in the table above, both conditions were satisfied.


Figure 66: DC Power Consumption [Dean]

Figure 66 shows all the calculations to verify that the circuit did not exceed the 50 mW power con-sumption limit.


Table 20 represents the frequency response data for the CE-CB cascode amplifier.

Table 20: Frequency Response Measured Values

Frequency (Hz) vout mV vU mV Gain (V/V) Gain (dB)LOW

30 662 91 7.27 17.2450 786 91 8.64 18.7381 1010 91 11.10 20.91110 1180 91 12.98 22.26140 1340 91 14.73 23.36

MID164 1400 91 15.38 23.74337 1830 91 20.11 26.07

1013 2000 91 21.98 26.8410094 1998 91 21.96 26.8341700 1998 91 21.96 26.83

102026 1996 91 21.93 26.82250344 1993 91 21.90 26.81507314 1760 91 19.34 25.73751425 1590 91 17.47 24.85955355 1400 91 15.38 23.74HIGH

1248299 1230 91 13.52 22.621506204 1090 91 11.98 21.572260929 794 91 8.73 18.823033402 624 91 6.86 16.723441028 560 91 6.15 15.78


Figure 67 represents the measured data collected in the lab. It includes the maximum and minimumallowed voltage gains prescribed by the requirements as well as the theoretical response based on pre-labcalculation data.

Figure 67: Frequency Response Plot [Dean]

6 ConclusionIn this lab, six varieties of amplifiers were constructed and had their performance investigated and com-pared. After characterizing these amplifiers, a cascode version of one of the previous two transistor am-plifiers was designed to meet a series of specification. It was constructed and tested in a similar fashion tothe amplifiers seen in the first part of this report.

The initial six amplifiers characterized included: 3 single amplifiers and 3 two stage amplifiers using acombination of the first three single amplifiers. The common emitter amplifier was found to produce alarge mid band gain, with a narrow bandwidth. It’s input and output impedance’s were both found tobe a moderate level. The common collector amplifier yielded a gain less than unity but functioned wellover a large bandwidth. This made the common collector a good choice as a buffer amplifier. It’s inputimpedance was large and its output impedance were found to be small which are consistent with goodcharacteristics for a buffer. The common base amplifier produced a gain less than unity due to the pres-ence of the degeneration resistor. Removing this resistor gives the amplifier the potential to achieve a gainlarger than unity. The input (due to generation resistor) and output impedance’s were also found to bemoderate, but this amplifier also functioned over a large bandwidth.

The two stage amplifiers were combinations of the single stage amplifiers aforementioned. The common


emitter - common base amplifier maintained a large gain with moderate input and output impedance’s.However, the addition of the common base amplifier increase the overall bandwidth of this amplifier. Thecommon collector - common base had a gain larger than unity, moderate input and output impedance’sbut the combination of the two produced a bandwidth larger than physically measurable in the lab. Thecommon collector - common emitter amplifier yielded a gain larger than unity - the large input of the com-mon collector, and moderate output of the common emitter amplifier. It had a large high frequency cutoffdue to the common collector stage. Combining the single stage amplifiers illustrated how the properties ofboth amplifiers individually contribute to even better more advanced functionality for the overall amplifier.

A cascode amplifier was built from a series of design constraints. There was a specific range for gainthat had to be met, restraints on the high and low frequency cutoff points as well as the power consump-tion. A preliminary design phase included theoretical calculations produced a design that ultimately hadto be modified based on real life values of components and physical behavior of the devices used. Vari-ations in assumptions taken in the initial calculations were factored in once testing began. The circuitthat was designed and tested met all the requirements set forth in the specifications. However, knowledgegained throughout this process would have led us to different design choices beforehand for improvedperformance and reliability. Planning to design for using one of either - RE2 or R4. Since both of thesecomponents reduce gain - it was difficult to find the balance using both in the design, when only one wouldhave sufficed. Removing RE2 and increasing R4 would have allowed for a larger voltage drop across thecollector of the common base stage, given a smaller drop across the emitter of the common emitter stage.The resultant voltage drop across RC would allow for a larger value for RC to maintain the desired 1mAof current in the collector branch. RC has a direct impact on increasing the gain of this amplifier whichwould have been a better design choice. This would have produced an overall better amplifier - regardlessof the goal of obtaining a specific gain as in this case (RE2 could be adjusted to achieve the desired gain).

References[1] ELEC 3905 Manual F2014. Ottawa: Carleton University, 2014. 9. Web. 4 Nov. 2014


ELEC3509_Lab2

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