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For a single stage CE amplifier, gm = 50 mA/V, Ce= 1 pF and Cc = 0.2 pF. The frequency at which the short circuit common-emitter current gain attains unit magnitude is given by
- a)2.2 GHz
- b)3.3 GHz
- c)5.5 GHz
- d)6.6 GHz
Correct answer is option 'D'. Can you explain this answer?
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For a single stage CE amplifier, gm = 50 mA/V, Ce= 1 pF and Cc = 0.2 p...
The frequency at which the short circuit common- emitter current gain attains unit magnitude is given by
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For a single stage CE amplifier, gm = 50 mA/V, Ce= 1 pF and Cc = 0.2 p...
To determine the frequency at which the short circuit common-emitter current gain attains unit magnitude, we need to analyze the amplifier circuit.
CE Amplifier Circuit:
The CE (common-emitter) amplifier is a basic configuration of a transistor amplifier. It consists of a bipolar junction transistor (BJT) in the common-emitter configuration, along with input and output capacitors.
Given Parameters:
- Transconductance (gm) = 50 mA/V
- Input Capacitance (Ce) = 1 pF
- Output Capacitance (Cc) = 0.2 pF
Analysis:
1. Frequency Response:
The frequency response of the CE amplifier is determined by the input and output capacitances. The cutoff frequency, fc, is the frequency at which the gain drops to 1/sqrt(2) or -3 dB.
2. Short Circuit Common-Emitter Current Gain:
The short circuit common-emitter current gain, hfe, is given by the following equation:
hfe = gm * (1 + gm * Re)
Where Re is the emitter resistance. In this case, we can assume Re to be zero for simplicity.
3. Unity Gain Frequency:
The unity gain frequency, ft, is the frequency at which the short circuit common-emitter current gain, hfe, becomes unity (1).
Calculation:
To calculate the unity gain frequency, we need to set hfe = 1 and solve for the frequency.
hfe = gm * (1 + gm * Re)
1 = gm * (1 + gm * Re)
1 = gm + gm^2 * Re
gm^2 * Re = 1 - gm
Re = (1 - gm) / gm^2
Substituting the given value of gm (50 mA/V), we can calculate the value of Re.
Re = (1 - 0.05 A/V) / (0.05 A/V)^2
Re = 19.8 Ω
Now, we can calculate the unity gain frequency (ft) using the following equation:
ft = 1 / (2π * (Ce + Cc) * Re)
Substituting the given values of Ce (1 pF), Cc (0.2 pF), and Re (19.8 Ω), we can calculate the unity gain frequency (ft).
ft = 1 / (2π * (1 pF + 0.2 pF) * 19.8 Ω)
ft ≈ 6.6 GHz
Therefore, the frequency at which the short circuit common-emitter current gain attains unit magnitude is approximately 6.6 GHz. Hence, the correct answer is option 'D'.
CE Amplifier Circuit:
The CE (common-emitter) amplifier is a basic configuration of a transistor amplifier. It consists of a bipolar junction transistor (BJT) in the common-emitter configuration, along with input and output capacitors.
Given Parameters:
- Transconductance (gm) = 50 mA/V
- Input Capacitance (Ce) = 1 pF
- Output Capacitance (Cc) = 0.2 pF
Analysis:
1. Frequency Response:
The frequency response of the CE amplifier is determined by the input and output capacitances. The cutoff frequency, fc, is the frequency at which the gain drops to 1/sqrt(2) or -3 dB.
2. Short Circuit Common-Emitter Current Gain:
The short circuit common-emitter current gain, hfe, is given by the following equation:
hfe = gm * (1 + gm * Re)
Where Re is the emitter resistance. In this case, we can assume Re to be zero for simplicity.
3. Unity Gain Frequency:
The unity gain frequency, ft, is the frequency at which the short circuit common-emitter current gain, hfe, becomes unity (1).
Calculation:
To calculate the unity gain frequency, we need to set hfe = 1 and solve for the frequency.
hfe = gm * (1 + gm * Re)
1 = gm * (1 + gm * Re)
1 = gm + gm^2 * Re
gm^2 * Re = 1 - gm
Re = (1 - gm) / gm^2
Substituting the given value of gm (50 mA/V), we can calculate the value of Re.
Re = (1 - 0.05 A/V) / (0.05 A/V)^2
Re = 19.8 Ω
Now, we can calculate the unity gain frequency (ft) using the following equation:
ft = 1 / (2π * (Ce + Cc) * Re)
Substituting the given values of Ce (1 pF), Cc (0.2 pF), and Re (19.8 Ω), we can calculate the unity gain frequency (ft).
ft = 1 / (2π * (1 pF + 0.2 pF) * 19.8 Ω)
ft ≈ 6.6 GHz
Therefore, the frequency at which the short circuit common-emitter current gain attains unit magnitude is approximately 6.6 GHz. Hence, the correct answer is option 'D'.
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For a single stage CE amplifier, gm = 50 mA/V, Ce= 1 pF and Cc = 0.2 pF. The frequency at which the short circuit common-emitter current gain attains unit magnitude is given bya)2.2 GHz b)3.3 GHzc)5.5 GHz d)6.6 GHzCorrect answer is option 'D'. Can you explain this answer?
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