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BJT and JFET Frequency Response

High-pass RC filter

For the circuit on the left, let us calculate the voltage gain A = vo/vi. However as the impedance of the capacitor changes with the frequency the gain changes with the frequency.

A() is called frequency response of the filter circuit above. As the frequency response A() is complex, it has a magnitude and phase.

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So, let us calculate the cut-off frequency c for the high-pass circuit on the previous slide.

The frequency where the output power drops to half (of the maximum output power) is called the cut-off frequency, c. Thus, at the cut-off frequency, the output voltage gain magnitude square will drop to half. As, in this case the maximum gain is one,

Thus, frequency response of the high-pass filter A() is given by

High-pass RC filter Magnitude and Phase Response

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Low-pass RC filter

For the circuit on the left, let us calculate the voltage gain A = vo/vi. However as the impedance of the capacitor changes with the frequency the gain changes with the frequency.

A() is called frequency response of the filter circuit above. As the frequency response A() is complex, it has a magnitude and phase.

So, let us calculate the cut-off frequency c for the low-pass circuit on the previous slide.

The frequency where the output power drops to half (of the maximum output power) is called the cut-off frequency, c. Thus, at the cut-off frequency, the output voltage gain magnitude square will drop to half. As, in this case the maximum gain is one,

Thus, frequency response of the low-pass filter A() is given by

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Low-pass RC filter Magnitude and Phase Response

dB (Decibels)

The decibel (dB) is a logarithmic unit used to express the ratio of two values of a physical quantity, often power or intensity. One of these values is often a standard reference value, in which case the decibel is used to express the level of the other value relative to this reference.

Magnitude response in decibels is given by

So, the cut-off frequency for the scaled magnitude response is 1/ 2. Thus, in dBs:

And the scaled magnitude response (maximum value is 1) in decibels is given by

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General Frequency Considerations

Frequency response of an amplifier refers to the frequency range in which the amplifier will operate with negligible effects from capacitors and capacitance in devices.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 will lower the gain.At high frequencies stray capacitances associated with the active device will lower the gain.Also cascading amplifiers will limit the gain at high and low frequencies.

Bode Plot

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).

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Cutoff Frequencies

The mid-range frequency of an amplifier is called the Bandwidth of the amplifier.The Bandwidth is defined by the Lower and Upper Cutoff frequencies.

Cutoff: frequency at which the gain has dropped by:

0.5 power0.707 voltage-3dB

Low Frequency Response – BJT Amplifier

At low frequencies Coupling capacitors (Cs, CC) and Bypass capacitors (CE) will have capacitive reactances (XC) that affect the circuit impedances.

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Coupling Capacitor - Cs

The cutoff frequency due to Cs can be calculated:

using

Coupling Capacitor - CC

The cutoff frequency due to CC can be calculated:

using

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Bypass Capacitor - CE

The cutoff frequency due to CE can be calculated:

using

where

Bode Plot of Low Frequency Response – BJT Amplifier

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.

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Roll-off of Gain in the Bode Plot

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.

-dB/Decade

-dB/Decade refers to the attenuation for every 10-fold change in frequency.For Low Frequency Response attenuations it refers to the loss in gain from the lower cutoff frequency to a frequency 1/10th the lower cutoff frequency.In the above drawn example:

fLS = 9kHz gain is 0dBfLS / 10 = .9kHz gain is –20dB

Therefore the roll-off is 20dB/decade. The gain decreases by –20dB/Decade.

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-dB/Octave

-dB/Octave refers to the attenuation for every 2-fold change in frequency.For Low Frequency Response attenuations it refers to the loss in gain from the lower cutoff frequency to a frequency 1/2 the lower cutoff frequency.In the above drawn example:

fLS = 9kHz gain is 0dBfLS/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.

Low Frequency Response – FET AmplifierAt low frequencies Coupling capacitors (CG, CC) and Bypass capacitors (CS) will have capacitive reactances (XC) that affect the circuit impedances.

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Coupling Capacitor - CG

The cutoff frequency due to CG can be calculated:

using

Coupling Capacitor - CC

The cutoff frequency due to CC can be calculated:

using

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Bypass Capacitor - CS

The cutoff frequency due to CS can be calculated:

using

Bode Plot of Low Frequency Response – FET Amplifier

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.

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Miller Effect Capacitance

Any P-N junction can develop capacitance. This was mentioned in the chapter on diodes.

In a BJT amplifier this capacitance becomes noticeable between: the Base-Collector junction at high frequencies in CE BJT amplifier configurations

and the Gate-Drain junction at high frequencies in CS FET amplifier configurations.

It is called the Miller Capacitance. It effects the input and output circuits.

Miller Input Capacitance (CMi)

It can be calculated:

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

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Miller Output Capacitance (CMo)

It can be calculated:

If the gain (Av) is considerably greater than 1:

High-Frequency Response – BJT Amplifiers

Capacitances that will affect the high-frequency response:

• Cbe, Cbc, Cce – junction capacitances• Cwi, Cwo – wiring capacitances• Cs, CC – coupling capacitors• CE – bypass capacitor

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High-Frequency Cutoff – Input Network (fHi)

using

and

High-Frequency Cutoff – Output Network (fHo)

using

and

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hfe (or ) Variation

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

Full Frequency Response of a BJT Amplifier

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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High-Frequency Response – FET Amplifier

Capacitances that will affect the high-frequency response:• Cgs, Cgd, Cds – junction capacitances• Cwi, Cwo – wiring capacitances• CG, CC – coupling capacitors• CS – bypass capacitor

High-Frequency Cutoff – Input Network (fHi)

using

and

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High-Frequency Cutoff – Output Network (fHo)

using

and

Multistage Frequency Effects

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.

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Total Frequency Response of a Multistage Amplifier

Once the cutoff frequencies have been determined for each stage (taking into account the shared capacitances), they can be plotted.

Again note the highest Lower Cutoff Frequency (fL) and the lowest Upper Cutoff Frequency (fH)

are closest to the actual response of the amplifier.

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).

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Square Wave Response Waveforms

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.