Chapter-3

Wide-Band Amplifiers

INTRODUCTION• High frequency communication circuits requires

amplifiers.– Mixer output– IF amplifiers– Output of modulator / demodulator– Repeaters– Power amplifiers– Video amplifiers

• All amplifiers have a high frequency limit beyond which it does not provided the needed gain.

• In designing of amplifiers , the frequency response of amplifiers have to be considered.

IntroductionFrequency Response of various amplifiers are found in this chapter• High frequency model of BJT.• High frequency model of FET.• Miller Theorem• High Frequency Analysis of BJT Amplifier• High Frequency Analysis of FET Amplifier• Broadbanding techniques

– Input Compensation– Feedback– Neutralization

• Cascode Amplifier

High Frequency Performance OF BJT

• Low frequency model of BJT

Where rπ is the input resistance

gm is the transconductance

High frequency model

Where rπ is the input resistance ro is the output resistance

c π is the base to emitter terminal capacitance cμ is the base to collector terminal capacitance co is the collector to emitter terminal capacitance

Analysis:

• Common emmiter short circuit current gain (Ai )

• Unity gain frequency (fT )• -3dB frequency

Derivations

From the above equations it is seen that:• at low frequencies the short circuit current gain is β•At higher frequencies the gain is reduced by due to c π and cμ .

At high frequency, the short circuit current gain

Analysis of the high frequency current gain

Unity Gain Frequency

• Bandwidth = ωβ

• Unity Gain Frequency = ωT

Current Gain-Bandwidth Product

The Unity Gain Frequency , ωT is also called as

Current Gain Bandwidth Product

fβ is the bandwidth

β is the gain

Therefore fT is referred to as the current gain bandwidth product of the device

Significance of fT The gain bandwidth product fT can be readily used to find the current gain at any frequency

Since,

At frequency below ωβ short circuit current gain is constant =

At frequency above ωβ short circuit current gain is readily determined by

Therefore knowledge of ωT allows us to find the gain at any given frequency ω

Problem-1

Short circuit current gain Ai is determined by

Given Data:Ic = 10 mA, β = 100, fT = 3 x 108 Hz, Cμ = 4pF

Contd:

Conclusion of High Frequency BJT analysis

At high frequency, the short circuit current gain

Analysis of the high frequency current gain

Unity Gain Frequency

Plot of Current Gain

Current Gain-Bandwidth Product

High Frequency Analysis of FET

Small Signal , Low Frequency model

High Frequency Model

From such analysis the Unity Gain Frequency for JFET can be written as

The only difference is that the resistor rπ is included in the model for bipolar transistorThe mid frequency input impedance of the common emmiter amplifier is rπ Ω.

Whereas the mid frequency input impedance of the common source amplifier is ∞.

The output circuits of the two devices are the sameThe high frequency analysis of JFET model is similar to Bipolar model to obtain the frequency response

Conclusion of High Frequency FET analysisHigh Frequency FET model

Current Gain-Bandwidth Product

Short Circuit Current Gain

Plot of Current gain

Miller Theorem

Equivalent Circuit

An equivalent circuit of the amplifier with feedback resistor

Equivalent Circuit

High Frequency Analysis of FET Amplifier

High Frequency Model of FET

Applying MILLER’S THEOREM to the feedback capacitor Cgd

Voltage gain at low frequency without considering the effects of parasitic capacitance

Frequency Analysis of FET AmplifierPlot of Voltage gain v/s Frequency

Vo = I x RL’

Output side

Input Side

Vg= I x Rg

I = Vi / (R + Rg )

Vg = [Vi / (R + Rg )] x Rg

Low Frequency Voltage Gain

Miller Effect Limits the performance of High voltage gain amplifier• To find the voltage gain Av , the equivalent fig. seen is simplified as

High Frequency analysis of High voltage gain FET amplifier

VTH = Vi

Derivation of High frequency Voltage Gain

High Frequency Equivalent Circuit

To find input voltage Vi

Apply Voltage divider theorem

VOLTAGE GAIN AT HIGH FREQUENCY (Common Source FET Amplifier)

VOLTAGE GAIN AT LOW FREQUENCY(Common Source FET Amplifier)

Frequency Response Analysis of the derived voltage gain

• Plotting the frequency dependent voltage gain v/s frequency and determining the upper cutoff frequency

The high frequency pole due to the input circuit. The high frequency pole due to the output circuit.

GAIN AT HIGH FREQUENCY

The two high frequency poles are at ω1 and ω2.

ω1 is the high frequency pole due to the input circuit.

ω2 is the high frequency pole due to the output circuit.

Significance of the two poles studied

• Miller effect leads to high value of CT

( as the input capacitance is amplified by the voltage gain)• CT is larger than Co .

(as CT is amplified by the voltage gain.)• Hence ω1 is much smaller than the ω2 value unless R is very

small.

ANALYSIS SHOWS THAT THE UPPER FREQUENCY LIMIT OF THE AMPLIFIER IS USUALLY DETERMINED BY

THE POLE OF THE INPUT CIRCUIT

Since ω1 < ω2 , The upper cutoff frequency of the voltage gain is determined by ω1

Significance of ω1, is that it is the plot of gain is almost constant (low frequency voltage gain ) till ω1 and reduces by 0.707 Avmax at ω1

Therefore , high value of CT , limits the frequency reponse of the common source amplifier circuit

Problem

The High frequency equivalent circuit with the given data

Solution

Problem on Common Emitter BJT amplifier

For analysis we apply Miller theorem

Simplified equivalent

To Plot the Frequency response

Mid Frequency Voltage Gain

Mid Frequency Voltage Gain is frequency independent term

Therefore we can neglect the effect of parasitic capacitances

Vo = (gm V ) 600

Where, V = Vth

Common Base BJT amplifier

• Common Base amplifiers are used in many high frequency applications because they have a wider bandwidth than does a equivalent common emitter amplifier has.

• In CB configuration the i/p impedance is relatively small and output impedance is quite large.

• Typical values of ri is few Ω to maximum of 50 Ω

ro is from ∞ (i.e in MΩ range)

i.e the input capacitance reduces

This effectively causes the gain of the CB amplifier to be lesser than the CE amplifier (because of low input impedance) and BW is wider than CE configuration

This leads to an increase in cutoff frequency ω1

For CE amplifier : Voltage G ain

For CB amplifier : Voltage Gain

CB amplifier has Wider Bandwidth than CE amplifier ?

Circuit diagram of CB amplifier

High frequency model

Apply Miller theorem

ro is very high ≈ ∞ (MHz) therefore ignored (ro in parallel with RL )

Analysis (for the corner frequencies)

Analysis can be done either by computing the gain Vo/Vi and then find ω1 and ω2.

Analysis can be done by analyzing the input and output circuit separately

Input circuit is analyzed to find ω1

Output circuit is analyzed to find ω2

Analysis of input circuit ( ω1)

Where,and,

Where,

Analysis of the output circuit

Similar to the analysis of the input circuit , the output circuit is analyzed to find Vo / I L in order to get the corner frequency due to the output circuit

Conclusion on the high frequency analysis of the common base BJT amplifier

Using approximations and Miller theorem

Analysis of input circuit gives

Analysis of output circuit gives ω2

High frequency model of CB amplifier

For Common Base Amplifier the output circuit corner frequency can be lower than the corner frequency of the input circuit

Problem

High frequency model of CB amplifier

Voltage Gain of CB amp. Is much less than that of CE amp.

Bandwidth of CB amp. is larger than CE amp.

BROADBANDING

• As gain increases miller capacitance increases and this capacitor invariably limits the upper frequency response of the amplifier

• In designing high frequency-high gain amplifier miller capacitor plays an important role in reducing the bandwidth

BROADBANDING Techniques are basically the techniques used for improving the frequency response of the basic amplifier circuit.

In Communication Circuits

• Narrowband amplifier: Which includes some type of tuned circuit.

• Wideband amplifier: Such as Video amplifiers in which it is necessary to maintain gain relatively constant over several decades of frequency.

• The bandwidth of single stage amplifier can be extended by adding frequency sensitive components to the circuits.

• This method is called as BROADBANDING.

High Frequency Analysis of Common Emitter BJT amplifier

The bandwidth of the CE amplifier is decided by the input Miller Capacitance (Cm)

Voltage Gain of CE amplifier is

High Frequency Analysis of Common Emitter BJT amplifier

Midband voltage gain

Bandwidth (cutoff frequency)

From the above equation it is seen that source impedance should be as small as possible to maximize the voltage gain and bandwidth

Broadbanding Techniques

To improve the frequency band few techniques are

• Input Compensation• Feedback techniques• Neutralization

Input Compensation

• Bandwidth can be extended by modifying the amplifier input circuit.

• Input Compensation is a method in which a capacitor Cs is added in parallel with the input resistance Rs

• Input Compensation is a method used to cancel the effect of miller capacitance (Cm) on the input with no reduction in voltage gain.

Basic Principle

By using input compensation method

The Bandwidth is determined by the output side of the circuit (ω2) and not by the input circuit ( ω1)

Where , ω2 > ω1

Design

Cs has to be selected such that :

The Bandwidth is determined by the output side of the circuit (ω2) and not by the input circuit ( ω1)

Neutralization

• The concept is to cancel out the feedback current flowing through the C μ with an equal and opposite current.

Neutralization is a wideband technique

• Neutralizing the parasitic capacitance Cμ , which appears between the input and the output terminals of the transistor.

Neutralization

In order to prevent these unnecessary oscillations,

neutralization is done in RF amplifiers

Voltage amplifier with Neutralization

• This is the most commonly used method of neutralization.

Working• CN = Neutralization Capacitor• Cμ = Parasitic capacitance

• Neutralizing Current flowing through CN (I CN ) will cancel out the current I Cμ .

• Hence the effect of Cμ on the output is overcome.

• However the circuit works fine if the parasitic capacitance is known precisely.

• Inaccuracy of the circuit may result in relatively narrowband amplifier

Second method of neutralization

• Value of L is chosen so that it forms a parallel tuned circuit with Cμ at the frequency of interest.

• Hence it provides high impedance at this frequency

• Thereby decoupling the input and the output side via Cμ.

Feedback

BLOCK DIAGRAM OF NEGATIVE FEEDBACK SYSTEM

Advantage of Negative feedback over Neutralization

Summary: Benefits of Negative Feedback

1) Gain desensitizationto transistor parameters

2) Bandwidth enhancementby the factor (1 + loop gain)

3) Modification of I/O impedances– Rin is increased by the factor (1 + loop gain)

– Rout is decreased by the factor (1 + loop gain)

4) Linearity improvement– Gain is more uniform for different signal levels.

Types of Feedback

Basic Principle

Current to Voltage Feedback(Feedback is a voltage α to output current)

• Here a voltage proportional to the load current is fedback to the input via emitter resistor RE

• This feedback

Increases the amplifier input impedance and decreases its output impedance

Common Emitter Amplifier with Current series Feedback

Without Feedback

Ce is called as the bypass capacitor

Vi = Vs

With Feedback

Vi = Vs - ieRe

Effective input voltage between the base and the emitter is reduced (NEGATIVE FEEDBACK)The feedback voltage ieRe is proportional to the output current (ie ≈ ic) (CURRENT SERIES FEEDBACK)

High Frequency Model

Frequency Analysis

Multiplying and dividing this equation with

The gain without feedback is

Therefore the feedback factor is

This Proves that with negative feedback

The midfrequency gain with feedback can be made independent of the transistor parameters.

Bandwidth

Which shows that the bandwidth can be made independent of the Miller capacitance

Voltage to Current Feedback

• The common emitter amplifier shown in figure generates a feedback current through the resistor RF which is proportional to output voltage.

• This feedback

Reduces the amplifier input impedance.

Mid Frequency Equivalent Circuit

Frequency Analysis

Features :

High Frequency Amplifier using MOSFET

Basic Common Source MOSFET amplifier

High Frequency Equivalent Circuit

Simplified Circuit (miller theorem)

Cutoff Frequency related to the input circuit

Cutoff Frequency related to the output circuit

Gain Bandwidth Product

• Midfrequency Voltage gain of the MOSFET is given by

• Therefore the gain bandwidth product can be written as

• Cutoff Frequency w.r.t input circuit

• Cutoff Frequency w.r.t output circuit

• Time constant of output RC network is higher than the time constant of the input RC network

• Therefore the cutoff frequency Fo (i.e bandwidth B) is the upper cutoff frequency of the amplifier

Bandwidth B =

CASCODE AMPLIFIER

A cascode amplifier has a high gainmoderately high input impedance high output impedance high bandwidth.

Cascode AmplifierThe analysis of single stage amplifier shows that• The upper frequency limit of the amplifier is usually

determined by the input circuit.

• The Bandwidth can be increased by decreasing the source resistance or by decreasing the voltage gain ( which reduces the Miller capacitance)

If neither of these reductions is possible:• Cascode amplifier meets the gain bandwidth specification.

• Cascode amplifieris a two stage amplifier consisting on a common emitter (or common source) amplifier followed by a common base (or common gate) amplifier..

Basic Concept• While the C-B (common-base) amplifier is known for wider bandwidth

than the C-E (common-emitter) configuration, the low input impedance (10s of Ω) of C-B is a limitation for many applications.

• The solution is to precede the C-B stage by a low gain C-E stage which has moderately high input impedance (kΩs).

• CB amplifier has better frequency response than CE amplifier

• CE amplifier is still preferred to have moderately high input impedance.

• The key is to reduce the gain of the CE amplifier ( to about 1) so that the miller effect on the input reduces.

Analysis of Cascode amplifier

Which is same as that realized by a single stage amplifier

But since the first stage (CE amplifier ) no longer has a gain greater than unity

The input miller capacitor of CE will decrease

Hence ω1 will increase as compared to ω2. ω1 > ω2.

Bandwidth of cascode amplifier is decided by the capacitance at the output.

The two stage amplifier has voltage gain same as that of a single stage amplifier with an appreciably wider bandwidth

REVIEW on Cascode Amplifier

A cascode amplifier consists of a common-emitter stage loaded by the emitter of a common-base stage.

The heavily loaded C-E stage has a low gain of 1, overcoming the Miller effect

A cascode amplifier has a high gain, moderately high input impedance, a high output impedance, and a high bandwidth.

Extra Notes

Application of Millers theorem to simplify the amplifier model

Where, K is the voltage gain between the two nodes