Chapter 9:

BJT and FET

Frequency Response

Brief Lecture Note/PPT

of

Analog Electronics

B.Tech.- Computer Science Engineering , Semester-IV, Session- 2018/19-22

Topic: Frequency Response of BJT and FET

By:

Amar Choudhary, Assistant Professor,

Dr. APJ Abdul Kalam Women's Institute of Technology, Darbhanga, Bihar

Research Scholar, Amity School of Engineering and Technology, Amity University

(Lucknow Campus), Noida, Uttar Pradesh- 226010

mail: amar.giet.ece@gmail.comRef: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

General Frequency Considerations

2Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

The frequency response of an amplifier refers to the frequency range in which the

amplifier will operate with negligible effects from capacitors and device internal

capacitance. This range of frequencies can be called the mid-range.

• At frequencies above and below the midrange, capacitance and any

inductance will affect the gain of the amplifier.

• At low frequencies the coupling and bypass capacitors lower the gain.

• At high frequencies stray capacitances associated with the active device lower

the gain.

• Also, cascading amplifiers limits the gain at high and low frequencies.

Bode Plot

3Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

A Bode plot indicates the

frequency response of an

amplifier.

The horizontal scale

indicates the frequency (in

Hz) and the vertical scale

indicates the gain (in dB).

Cutoff Frequencies

4Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

The mid-range frequency

range of an amplifier is

called the bandwidth of

the amplifier.

The bandwidth is defined

by the lower and upper

cutoff frequencies.

Cutoff – any frequency at

which the gain has

dropped by 3 dB.

BJT Amplifier Low-Frequency Response

5Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

At low frequencies, coupling

capacitor (CS, CC) and bypass

capacitor (CE) reactances

affect the circuit impedances.

Coupling Capacitor (CS)

The cutoff frequency due to CS can be calculated by

2(Rs Ri )CsLs

1f

where

R i R 1 || R 2 ||βre

6Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

2π(Ro RL )CcLC

1f

where

Ro RC || ro

Coupling Capacitor (CC)

The cutoff frequency due to CC can be calculated with

7Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

Bypass Capacitor (CE)

2πReCELE

1f

βe E e

RsR R || ( r )

and

Rs Rs || R1 || R 2

The cutoff frequency due to CE can be calculated with

where

8Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

BJT Amplifier Low-Frequency Response

9Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

The Bode plot indicates

that each capacitor may

have a different cutoff

frequency.

It is the device that has

the highest lower cutoff

frequency (fL) that

dominates the overall

frequency response of the

amplifier.

Roll-Off of Gain in the Bode Plot

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

The Bode plot not only

indicates the cutoff

frequencies of the various

capacitors it also indicates

the amount of attenuation

(loss in gain) at these

frequencies.

The amount of attenuation

is sometimes referred to as

roll-off.

The roll-off is described as

dB loss-per-octave or dB

loss-per-decade.

Roll-off Rate (-dB/Decade)

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

-dB/decade refers to the

attenuation for every 10-fold

change in frequency.

For attenuations at the low-

frequency end, it refers to

the loss in gain from the

lower cutoff frequency to a

frequency that is one-tenth

the cutoff value.

In this example:

fLS = 9kHz gain is 0dB

fLS/10 = .9kHz gain is –20dB

Thus the roll-off is 20dB/decade

The gain decreases by –20dB/decade

Roll-Off Rate (–dB/Octave)

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

-dB/octave refers to the

attenuation for every 2-fold

change in frequency.

For attenuations at the low-

frequency end, it refers to

the loss in gain from the

lower cutoff frequency to a

frequency one-half the cutoff

value.

In this example:

fLS = 9kHz gain is 0dB

fLS / 2 = 4.5kHz gain is –6dB

Therefore the roll-off is 6dB/octave.

This is a little difficult to see on this graph because

the horizontal scale is a logarithmic scale.

BJT Low Frequency Example

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

BJT Low Frequency Example

-b) Sketch the frequency response using Bode plot

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

FET Amplifier Low-Frequency Response

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

At low frequencies,

coupling capacitor (CG,

CC) and bypass capacitor

(CS) reactances affect the

circuit impedances.

Coupling Capacitor (CG)

2π(Rsig Ri )CGLC

1f

where

Ri RG

The cutoff frequency due to

CG can be calculated with

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

Coupling Capacitor (CC)

2π(RoRL)CCLC

1f

where

Ro RD || rd

The cutoff frequency due to

CC can be calculated with

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

Bypass Capacitor (CS)

2πReqCSLS

1f

rd Ωgm

Seq1

R ||R

The cutoff frequency due to

CS can be calculated with

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

where

FET Amplifier Low-Frequency Response

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

The Bode plot indicates that

each capacitor may have a

different cutoff frequency.

The capacitor that has the

highest lower cutoff

frequency (fL) is closest to the

actual cutoff frequency of the

amplifier.

FET Low Frequency Example

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

FET Low Frequency Example

-b) Sketch the frequency response using Bode plot

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

Miller Capacitance

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

Any p-n junction can develop capacitance. In a BJT amplifier,

this capacitance becomes noticeable across:

• The base-collector junction at high frequencies in

common-emitter BJT amplifier configurations

• The gate-drain junction at high frequencies in common-

source FET amplifier configurations.

These capacitances are represented as separate input and output

capacitances, called the Miller Capacitances.

Miller Input Capacitance (CMi)

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

CMi (1 A v )Cf

Note that the amount of

Miller capacitance is

dependent on inter-

electrode capacitance

from input to output (Cf)

and the gain (Av).

Miller Output Capacitance (CMo)

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

If the gain (Av) is

considerably greater

than 1, then

CMo Cf

BJT Amplifier High-Frequency Response

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

Capacitances that affect the

high-frequency response are

• Junction

capacitances Cbe,

Cbc, Cce

• Wiring

capacitances

Cwi, Cwo

• Coupling

capacitors CS,

CC

• Bypass

capacitor CE

Input Network (fHi) High-Frequency Cutoff

2πRThiCiHi

1f

where

RThi Rs || R1 || R 2 || Ri

Ci CWi Cbe CMi

CWi Cbe (1 Av )Cbc

and

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

Output Network (fHo) High-Frequency Cutoff

where

RTho RC || RL || ro

and

Co CWo Cce CMo

2πRThoCoHo

1f

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

hfe (or )Variation

The hfe parameter (or ) of a

transistor varies with

frequency

bc

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

mid e be

1fβ

2πβ r (C C )

BJT High Frequency Example

For the following circuit parameters,

a)Determine †H i and †Ho

†H i = 738.24 KHz, †Ho

=8.6MHz

b) Determine †Q and †T

†Q = 2. 52MHz

†T = 252 MHz

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

BJT Amplifier Frequency Response

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

Note the highest lower cutoff frequency (fL) and the lowest upper cutoff

frequency (fH) are closest to the actual response of the amplifier.

FET Amplifier High-Frequency Response

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

Capacitances that affect the

high-frequency response are

• Junction

capacitances Cgs,

Cgd, Cds

• Wiring

capacitances

Cwi, Cwo

• Coupling

capacitors CG,

CC

• Bypass

capacitor CS

Input Network (fHi) High-Frequency Cutoff

2πRThiCiHi

1f

Ci CWi Cgs CMi

CMi (1 A v )Cgd

RThi Rsig || RG

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

Output Network (fHo) High-Frequency Cutoff

2πRThoCoHo

1f

RTho R D || RL || rd

Co CWo Cds CMo

MoA

1CgdC 1

v

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

For the following circuit parameters,

a)Determine †H i and †Ho

†H i = 945.67 KHz, †Ho

=11.57MHz

FET High Frequency Example

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

Multistage Frequency Effects

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

Each stage will have its own frequency response,

but the output of one stage will be affected by

capacitances in the subsequent stage. This is

especially so when determining the high frequency

response. For example, the output capacitance(Co)

will be affected by the input Miller Capacitance

(CMi) of the next stage.

Multistage Amplifier Frequency Response

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

Once the cutoff frequencies have been determined for each stage (taking into

account the shared capacitances), they can be plotted.

Note the highest lower cutoff frequency (fL) and the lowest upper cutoff

frequency (fH) are closest to the actual response of the amplifier.

Multistage Amplifier Frequency Response

The total voltage gain for multistage with identical stages in low frequency is

given by

Av Av1n

= =Av,mid Av1,mid

1

1– j†1n

Which is equal to 1/sqrt(2) at cutoff so

The low cutoff frequency for the multistage can be derived as

1†u =

†1

21/n —1In similar way the high cutoff frequency for the multistage is given by

2†u = †1 21/n —1

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

Square Wave Testing

In order to determine the frequency response of an amplifier by experimentation,

you must apply a wide range of frequencies to the amplifier.

One way to accomplish this is to apply a square wave. A square wave consists of

multiple frequencies (by Fourier analysis: it consists of odd harmonics).

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

Square Wave Response Waveforms

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

If the output of the

amplifier is not a perfect

square wave then the

amplifier is ‘cutting’ off

certain frequency

components of the square

wave.

Square Wave Response Waveforms

Rising time vr is time needed by the signal to

raise from 10% to 90% from the maximum

value.

fs

The bandwidth is given by

BW = †H =0.35

vr

The low cutoff frequency is given byP

†L = g†s

V s

F

Where P =V–V

and † is the square wave

frequency.

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky

Square Wave Response Waveforms

Ref: Electronic Devices and Circuit Theory, 10/e Robert L. Boylestad and Louis Nashelsky