bjt and jfet frequency response
TRANSCRIPT
BJT and JFET
Frequency Response
Contents
Logarithm and dB Low frequency analysis-Bode plot Low frequency response-BJT and FET
amplifiers Miller effect capacitance High frequency response-BJT and FET
amplifiers Multistage frequency effects Square wave testing
Low Frequency Response – BJT Amplifier
At low frequencies Coupling capacitors (Cs, CC) and Bypass capacitors (CE) will have capacitive reactance (XC) that affect the circuit impedances.
Coupling Capacitor - CSThe cutoff frequency due
to CS can be calculated:
using
sLs
Ri)C(Rs2
1f
βre||R2||R1Ri
Coupling Capacitor - CC
The cutoff frequency due
to CC can be calculated:
using
)CcRRo(2
1f
LLC
π
oC r||RRo
Bypass Capacitor - CEThe cutoff frequency due to CEcan be calculated:
using
where
EeLE
CR2
1f
π
)rβ
sR(||RR eEe
R2||R1||RssR
Examplea. Determine the lower cutoff freq. for the
network of Fig. 1 using the following parameters:
Cs = 10μF, CE = 20μF, Cc = 1μF
Rs = 1KΩ, R1= 40KΩ, R2 = 10KΩ,
RE = 2kΩ, RL = 2.2KΩ,
β = 100, r0 = ∞Ω, Vcc = 20V
b. Sketch the frequency response using a Bode plot
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 of the low cutoff frequency (fL) that dominates the overall frequency response of the amplifier (fLE).
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 –20dBTherefore the roll-off is 20dB/decade. The gain decreases by –20dB/Decade.
-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 –6dBTherefore 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.
Coupling Capacitor - CGThe cutoff frequency due
to CG can be calculated:
using
GLG
Ri)C(Rsig2
1f
π
GRRi
Coupling Capacitor - CC
The cutoff frequency due
to CC can be calculated:
using
CLLC
)CR(Ro2
1f
π
dD r||RRo
Bypass Capacitor - CSThe cutoff frequency due to CS canbe calculated:
where
using
Seq
LSCR2
1f
π
)///()1(1 LDddmS
Seq RRrrgR
RR
Ωr g
1||RR
dmSeq
Example
a. Determine the lower cutoff freq. for the network of Fig. 2 using the following parameters:
CG = 0.01μF, Cc = 0.5μF, Cs = 2μF
Rsig = 10KΩ, RG= 1MΩ, RD = 4.7KΩ,
RS = 1kΩ, RL = 2.2KΩ, IDSS = 8mA,
Vp = -4V, rd = ∞Ω, VDD = 20V
b. Sketch the frequency response using a Bode plot
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.
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: [Formula 11.42]
Note that the amount of Miller Capacitance is dependent on interelectrode capacitance from input to output (Cf) and the gain (Av).
fMi Av)C(1C
Miller Output Capacitance (CMo)
It can be calculated: [Formula 11.43]
If the gain (Av) is considerably greater than 1: [Formula 11.44]
fMo )CAv
1(1C
fMo CC
High-Frequency Response – BJT Amplifiers
Capacitances that will affect the high-frequency response:
• Cbe, Cbc, Cce – internal capacitances• Cwi, Cwo – wiring capacitances• CS, CC – coupling capacitors• CE – bypass capacitor
High-Frequency Cutoff – Input Network (fHi)
using and
iThiHi
CR2
1f
π
re||R||R||RsR 21Thi
Av)Cbc(1CbeCCCbeCCi WiMiWi
High-Frequency Cutoff – Output Network (fHo)
using and MoWo CCceCCo
oLCTho r||R||RR
CoR2
1f
ThoHo
π
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
iThiHi
CR2
1f
π
GsigThi R||RR
MigsWii CCCC
gdMi Av)C(1C
High-Frequency Cutoff – Output Network (fHo)
using and
oThoHo
CR2
1f
π
dLDTho r||R||RR
ModsWoo CCCC
gdMo )CAv
1(1C
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.
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).
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.