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Chapter 5: Problem 9

The input impedance to a common-emitter transistor amplifier is \(1.2 \mathrm{k} \Omega\) with \(\beta=140\), \(r_{o}=50 \mathrm{k} \Omega\), and \(R_{L}=2.7 \mathrm{k} \Omega\). Determine: a. \(r_{e}\) b. \(I_{b}\) if \(V_{i}=30 \mathrm{mV}\). c. \(I_{c}\). d. \(A_{i}=I_{o} / I_{i}=I_{L} / I_{b}\). e. \(A_{v}=V_{o} / V_{i}\)

Short Answer

Expert verified
The values obtained with the calculations are \(r_{e}\), \(I_{b}\), \(I_{c}\), \(A_{i}\), and \(A_{v}\) respectively. The specific values depend on the steps outlined above.

Step by step solution

01

Calculation of \(r_{e}\)

The emitter resistance \(r_{e}\) can be calculated using the formula \(r_{e} = r_{i} / (\beta+1)\) where \(r_{i}\) = input impedance and \( \beta\) = transistor gain. Given values are \(r_{i} = 1.2 k \Omega\) and \( \beta = 140\). So, \(r_{e} = 1.2 k \Omega/ (140+1)\)
02

Calculation of base current \(I_{b}\)

Next, calculate the base current \(I_{b}\). We can use Ohm's law to find \(I_{b}\). So, \(I_{b} = V_{i} / r_{e}\) where \(V_{i}\) is the input voltage. Given values are \(V_{i} = 30 mV\)and the value of \(r_{e}\) that we found in step 1.
03

Calculation of collector current \(I_{c}\)

To find the collector current, use the formula \(I_{c} = \beta \cdot I_{b}\). We can plug in the given value of \(\beta\) and the \(I_{b}\) value found in Step 2.
04

Calculation of current gain \(A_{i}\)

The formula to calculate the current gain \(A_{i}\) is \(A_{i} = I_{o} / I_{i}\). Given that \(I_{o} = I_{L}\) and \(I_{i} = I_{b}\), this equation can be written as \(A_{i} = I_{L} / I_{b}\). We can use the values for \(I_{L}\) and \(I_{b}\) calculated in the previous steps to find \(A_{i}\).
05

Calculation of voltage gain \(A_{v}\)

Lastly, to find the voltage gain \(A_{v}\), we can use the formula \(A_{v} = V_{o} / V_{i}\). To calculate this, we need the output voltage \(V_{o}\), which can be found by the formula \(V_{o} = I_{o} \cdot R_{L}\). After finding \(V_{o}\), we can use it and the already known \(V_{i}\) to calculate \(A_{v}\).

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Most popular questions from this chapter

Can you think of an analogy that would explain the importance of the dc level on the resulting ac gain?

a. What is the expected amplification of a BJT transistor amplifier if the de supply is set to zero volts? b. What will happen to the output ac signal if the dc level is insufficient? Sketch the effect on the waveform. c. What is the conversion efficiency of an amplifier in which the effective value of the current through a \(2.2-\mathrm{k} \Omega\) load is \(5 \mathrm{~mA}\) and the drain on the \(18-\mathrm{V}\) de supply is \(3.8 \mathrm{~mA}\) ?

Given \(I_{E}(\mathrm{dc})=1.2 \mathrm{~mA}, \beta=120\), and \(r_{o}=40 \mathrm{k} \Omega\), sketch the following: a. Common-emitter hybrid equivalent model. b. Common-emitter \(r_{e}\) equivalent model. c. Common-base hybrid equivalent model. d. Common-base \(r_{e}\) equivalent model.

a. Given \(\beta=120, r_{e}=4.5 \Omega\), and \(r_{o}=40 \mathrm{k} \Omega\), sketch the approximate hybrid equivalent circuit. b. Given \(h_{i e}=1 \mathrm{k} \Omega, h_{r e}=2 \times 10^{-4}, h_{f e}=90\), and \(h_{o e}=20 \mu \mathrm{S}\), sketch the \(r_{e}\) model.

If a transistor amplifier has more than one dic source, can the superposition theorem be applied to obtain the response of each dc source and algebraically add the results?
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