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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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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,
So, let us calculate the cut-off frequency c for the high-pass circuit on the previous slide.
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.
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,
So, let us calculate the cut-off frequency c for the low-pass circuit on the previous slide.
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
And the scaled magnitude response (maximum value is 1) in decibels is given by
So, the cut-off frequency for the scaled magnitude response is 1/ 2. Thus, in dBs:
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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 power
0.707 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 0dB
fLS / 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 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.
Low Frequency Response – FET Amplifier
At 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.
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