## Introduction

Explore the intricacies of the Frequency Response of Amplifiers with our comprehensive study notes for EE/EC. Gain insights into gain, phase shift, and bandwidth for optimal circuit design and performance.

- Amplifiers do not have the same gain at all frequencies.
- An amplifier designed for radio frequencies will amplify a band of frequencies above about 100kHz but will not amplify the lower-frequency audio signals.
- In each case the amplifier has a particular frequency response, being a band of frequencies where it provides adequate amplification, and excluding frequencies above and below this band, where the amplification is less than adequate.

## Hybrid Equivalent Circuit for a Transistor

Understanding the Hybrid Equivalent Circuit for a transistor is essential for electrical and electronic engineering students. This study notes provide a comprehensive overview, enabling you to analyze transistor behavior and design efficient circuits.

- Any single-stage transistor amplifier, whether CB, CE or CC may be put in a standard form for small signal analysis so as to be able to identifyVg, Rg, andRLas well as the transistor’s input and output terminals.
- The hybrid equivalent circuit for a transistor consists of a Thevenin equivalent circuit at the input and a Norton equivalent circuit at the output.
- The equations relating the input and output voltages and currents in a transistors small signal equivalent circuit are given by
- hi= Input impedance
- hr= Reverse voltage ratio
- hf= Forward current transfer ratio
- h0= Output admittance
- where,hi,hr,hfandh0are theh-parameters and have a second subscript ofb, eorcaccording to the amplifier in question.
- Theh-parameters may be obtained from the transistor’s characteristic curve or may be measured experimentally by using changes in current and voltage levels to stimulate AC conditions.
- Typicalh-parameter values for CB, CE and CC connections are shown in the tables given below and are all dependent upon the collector current.

Typicalh-parameters for A 2N3391 Silicon Transistor,Evaluated at Ic= 1mA, VCE=5V, f=1kHz, and TA=25 degree Centrigrade

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Typicalh-parameters for A2N404 Germanium Transistor,Evaluated at Ic= 1mA, VCE=6V, f=1kHz, and TA=25 degree Centigrade.

If theh-parameters are given for one type of amplifier connection but are required for another type, the approximate conversion formulae in may be used.

Approximate Conversion Formulae for Transistor h-parameters

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- Knowing the h-parameters for a transistor, the values forAi, Ri, Av, RoAvgandAigmay be obtained using the exact equations in the tableby using a second subscript appropriate to the amplifier beinganalyzed. The value ofRgandRLis also necessary.
- Exact equations for the small signal analysis of transistor amplifiers

Using a transistor’sh-parameters, it is possible to dually matchRgandPLfor the Maximum Available Power Gain (MAG) from the transistor, Equations

- Where Δh= hiho-hohf

Circuit schematic hybrid model andV-I,h-parameter equations for the CE, CC and CB amplifier connections

- A transistor amplifier’s characteristics are very dependent upon the values used forRgandRL, but generally speaking, the characteristics may be summarized as in the given ahead.

Comparison between CB, CE, CC

Approximate equations forAi, Ri, AvandR0in terms of CEh-parameter are shown in table and are valid if,hoeRL≤0.1

- hoe=he=0
- Approximate equations forAi, Ri, AvandR0for CB, CE or CC amplifiers, given in terms of Ceh-parameters. To be used only when hoeRLor hoehe<=0.1 is given below

## Low-Frequency Response of Amplifier

- The value of the emitter bypass capacitor in a single-stage CE amplifier must be very large to provide a low value for the lower 3-dB frequency.f1equations forf1for different circuit conditions are summarized in the table.
- Summary of the approximate equations for mid-frequency voltage gain and lower 3-dB frequencyf1. For various circuit conditions:

- The electrolyte losses in the emitter bypass capacitor affect thelow-frequencyresponse somewhat but have a significant effect on mid-frequency gain.
- Low-frequencyresponse is also affected by the size of the coupling capacitors, as shown by

WhereR'iis the effective input resistance to the amplifier.

- The overall mid-frequency voltage gain of an amplifier consisting of cascaded CE stages is the product of the gains of all of the stages. But the overall current gain must take into account the load andbe biasingresistors, along with the transistor input impedances.
- Analysis of cascaded stages generally proceeds from the last stage back towards the input, by determiningAi, RiandAvin that order.
- The overalllow-frequencyresponse,f1(n) forncascaded stages each having the same value of f1 given by

which shows that thelow-frequencyresponse is poorer than for a single stage.

- The ability of an amplifier to handle a square wave signal is measured by the sag and is related to the amplifier's lower 3-dB frequency, f1by

where fis the frequency of the square wave. To provide a lowSagrequires a very low value forf1.

- Cascaded transformer coupled amplifiers designed for maximum power transfer conditions have equal current and voltage gains given by

- The lower 3-dB frequencyf1, for a transformer-coupled amplifier, is restricted by the transformer’s primary inductanceLp, as given by

WhereRis the effective portion of the transistor’s load and output resistance in parallel withLp.

- In order for a transformer-coupled amplifier to handle a pulse of durationtdwith less than a given amount ofSag, the transformer must have a minimum primary inductance is given by

## High-Frequency Response of Amplifiers

- The hybrid-πmodel of a transistor at high frequencies includes the capacitive effects of the p-n junction and involves a base spreading resistance that creates a virtual base.
- The transistor’s high-frequency parameters are given in the equations below and include the transistor's transconductance.
- The parameters for the approximate hybrid-πmodel may be obtained from the following equations. (Numerical values shown are for 1 2N 2218 silicon transistor with:

Cb’cis usually given in the transistor manual asCoband is the CB open circuit output capacitance Cb’emay be given by the manufacturer or it may be calculated using the equation given,ftis the frequency at which the CE short circuit current gain drops to unity.

- The transistor’s short circuit current gain varies with frequency and is characterized by theαcut-off andβcut-off frequencies, where the current gain drops by 3 dB from the value at mid frequencies in a CB and CE connection respectively.
- Important high-frequency characteristics of a transistor are ft, the gain bandwidth product and are defined to be the frequency at which a common emitter’s short circuit current gain drops to unity.
- Cascaded CE stages operating at high frequency have a reduced overall bandwidth given by

where n is the number of stages andf2is the bandwidth of each stage

- The ability of an amplifier to reproduce a square wave input with a low rise time, tr, is directly proportional to the bandwidthf2. That is

- When a transistor is operated at high frequencies with a resistive load, the collector-to-base junction capacitance appears as an enlarged value of capacitance at the input, thus reducing voltage and current gain below the values expected at theαandβ cut-off.
- The high-frequency response of a transformer-coupled amplifier is usually limited entirely by the transformer’s leakage inductance and distributed capacitance, which creates a series resonant effect.
- Transistor noise is usually measured as a spot noise figure, NF or as the average noise figure NF, with typical values between 0.5 and 5 dB depending upon the source resistance, collector current, and frequency.

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