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Facebook• At the high – frequency end, there are two factors that define the – 3dB cutoff point:
– The network capacitance ( parasitic and introduced) and
– the frequency dependence of hfe(b)
Network parameters
• In the high frequency region, the RC network of the amplifier has the configuration
shown below.
• At increasing frequencies, the reactance XC will decrease in magnitude, resulting
in a short effect across the output and a decreased gain.
Vo = Vi(-jXC) / R -jXC
Vo / Vi = 1/[ 1+j(R/XC)] ; XC = 1/2pfC
AV = 1/[ 1+j(2pfRC)];
AV = 1/[ 1+jf/f2]
o This results in a magnitude plot that drops off at 6dB / octave with increasing
frequency.
Network with the capacitors that affect the high frequency response
• Capacitances that will affect the high-frequency response:
· Cbe, Cbc, Cce – internal capacitances
· Cwi, Cwo – wiring capacitances
· CS, CC – coupling capacitors
· CE – bypass capacitor
The capacitors CS, CC, and CE are absent in the high frequency equivalent of the BJT
amplifier.The capacitance Ci includes the input wiring capacitance, the transition
capacitance Cbe, and the Miller capacitance CMi.The capacitance Co includes the
output wiring capacitance Cwo, the parasitic capacitance Cce, and the output Miller
capacitance CMo.In general, the capacitance Cbe is the largest of the parasitic
capacitances, with Cce the smallest.
As per the equivalent circuit,
fH = 1 / 2pRthiCi
Rthi = Rs|| R1||R2||Ri
Ci = Cwi+Cbe+CMi = CWi + Cbe+(1- AV) Cbe
At very high frequencies, the effect of Ci is to reduce the total impedance of the
parallel combination of R1, R2, Ri, and Ci.The result is a reduced level of voltage
across Ci, a reduction in Ib and the gain of the system.
For the output network,
fHo = 1/(2pRThoCo)
RTho = RC||RL||ro
Co = Cwo+Cce+CMo
At very high frequencies, the capacitive reactance of Co will decrease and
consequently reduce the total impedance of the output parallel branches.
The net result is that Vo will also decline toward zero as the reactance Xc becomes
smaller.The frequencies fHi and fHo will each define a -6dB/octave asymtote.
If the parasitic capacitors were the only elements to determine the high – cutoff
frequency, the lowest frequency would be the determining factor.However, the
decrease in hfe(or b) with frequency must also be considered as to whether its break
frequency is lower than fHi or fHo.
hfe (or ) variation
• The variation of hfe( or b) with frequency will approach the following relationship
hfe = hfe mid / [1+(f/fb)]
• fb is that frequency at which hfe of the transistor falls by 3dB with respect to its
mid band value.
• The quantity fb is determined by a set of parameters employed in the hybrid p
model.
• In the hybrid p model, rb includes the
• base contact resistance
• base bulk resistance
• base spreading resistance
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