Ch 9 Bjt Jfet Hz Response

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Chapter 9

Decibel (dB)◦ Level of gain◦ Relates input to output◦ Unless noted, log 푥 is assumed

푁 = 10

푥 = log 푁ECET 257 Consumer Power Electronics, PNC 2

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FIG. 21.1 Semilog graph paper.

ECET 257 Consumer Power Electronics, PNC 3

FIG. 21.2 Frequency log scale.


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1 Bel= 10 Decibels (dB) Power◦ 푑퐵 = ퟏퟎ log

Voltage◦ 푑퐵 = ퟐퟎ log


TABLE 21.1


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• At frequencies below mid-range, the coupling and bypass capacitors lower the gain.

• At frequencies above mid-range, stray capacitances associated with the active device lower the gain.

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

Frequency Response: The frequency range in which an amplifier will operate with negligible effects from capacitors and device internal capacitances; often called the mid-range.


푋 =

A Bode plot illustrates the frequency response of an amplifier.

The horizontal scale indicates the frequency (in Hz) and the vertical scale indicates the gain (in dB).


Fig. 9.8

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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 rate of attenuation is sometimes referred to as roll-off.

The roll-off is measured in dB-per-octave or dB-per-decade.


-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.

fLS = 9kHz gain is 0dBfLS/10 = .9kHz gain is –20dBThus the roll-off is −20dB/decade


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-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.

fLS = 9kHz gain is 0dBfLS / 2 = 4.5kHz gain is –6dBTherefore the roll-off is 6dB/octave.


The mid-range of an amplifier is called the bandwidth of the amplifier.

The bandwidth is defined by the lower and upper cutoff frequencies.

Cutoff frequency – any frequency at which the gain has dropped by 3 dB (70.7%) from its mid-range value


Fig. 9.8

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At low frequencies, the reactances of the coupling capacitors (CS, CC) and the bypass capacitor (CE) affect the circuit impedances.


푓 =1

2휋푅퐶

The cutoff frequency due to CS can be calculated using

where


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The cutoff frequency due to CC can be calculated using

where


The cutoff frequency due to CE can be calculated with

where

and


Re is the resistance as seen from CE

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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 low-frequency response of the amplifier.



Phase shift◦ 휃 = − tan

◦ 휃 = − tan -45 at 푓

푓 =1

2휋푅퐶

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Find◦ re◦ Zi◦ fLS◦ fLC◦ fLE◦ Low cut-off frequency

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At low frequencies, the reactances of the coupling capacitors (CG, CC) and the bypass capacitor (CS) affect the circuit impedances.


The cutoff frequency due to CG can be calculated with

where


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The cutoff frequency due to CC can be calculated with

where


The cutoff frequency due to CS can be calculated with

where


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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.



Find◦ VGSQ and IDQ◦ gmo and gm◦ AVMID◦ ZI◦ AVS◦ fLG, fLC, and fLS◦ Low cut-off frequency

rd = ∞Ω

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Any p-n junction can develop capacitance. This capacitance becomes noticeable across:

• The BJT base-collector junction in a common-emitter amplifier operating at high frequencies• The FET gate-drain junction in a common-source amplifier at high frequencies

These capacitances are represented as separate input and output capacitances, called the Miller capacitances.

THESE ARE NOT ACTUAL COMPONENTS, BUT A PHENOMENON THAT OCCURS IN THE

CIRCUIT


Note that the amount of Miller capacitance is dependent on inter-electrode capacitance from input to output (Cf) and the gain (Av).


Feedback Capacitance

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If the gain (Av) is considerably greater than 1, then


Junction capacitances◦ Cbe, Cbc, Cce

Wiring capacitances◦ Cwi, Cwo

Coupling capacitors◦ CS, CC

Bypass capacitor◦ CE


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where

and


where

and


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The hfe parameter (or ) of a transistor varies with frequency


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Note the highest lower cutoff frequency (fL) and the lowest upper cutoff frequency (fH) are closest to the actual response of the amplifier.


Junction capacitances◦ Cgs, Cgd, Cds

Wiring capacitances◦ Cwi, Cwo

Coupling capacitors◦ CG, CC

Bypass capacitor◦ CS


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휃 = tan

휃 = tan 푓 =1

2휋푅퐶


Find◦ fHI, fHO◦ High cut-off frequency◦ Gain Bandwidth rd = ∞Ω

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Each stage has its own frequency response, but the output of each stage is affected by capacitances in the subsequent stage. For example, the output capacitance (Co) is affected by the input Miller Capacitance (CMi) of the next stage.


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.


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Ch 9 Bjt Jfet Hz Response