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Chapter 5: Problem 63

Given the typical values of \(R_{L}=2.2 \mathrm{k} \Omega\) and \(h_{o e}=20 \mu \mathrm{S}\), is it a good approximation to ignore the effects of \(1 / h_{o e}\) on the total load impedance? What is the percentage difference in total loading on the transistor using the following equation? $$ \% \text { difference in total load }=\frac{R_{L}-R_{L} \|\left(1 / h_{o e}\right)}{R_{L}} \times 100 \% $$

Short Answer

Expert verified
The percentage difference in total load impedance due to ignoring the effects of \(1/h_{oe}\) is 7.19%. Given that this value is not negligible, it's not a good approximation to ignore the effects of \(1 / h_{oe}\) on the total load impedance.

Step by step solution

01

Compute \(1 / h_{oe}\)

We'll find the value of the inverse of \(h_{oe}\). Given \(h_{oe} = 20 μS\), thus \(1 / h_{oe} = 1 / (20 × 10^{-6}) = 50000\ Ω\).
02

Calculate total load with and without \(1 / h_{oe}\)

Referring to the given typical value, \(R_L = 2.2 kΩ = 2200 Ω\). When we ignore the effects of \(1 / h_{oe}\) on the total load impedance, the load \(R_L\) is just \(2200 Ω\). When we consider the effects of \(1 / h_{oe}\) on the total load impedance, \(R_L\) should be calculated as \(R_L || (1 / h_{oe}) = R_L × (1 / h_{oe}) / [R_L + (1 / h_{oe})] = 2200 × 50000 / (2200 + 50000) = 2041.86 Ω\).
03

Calculate the percentage difference in total load

We substitute the calculated values into the formula in the exercise and find: % difference in total load \(= (R_{L}-R_{L|| (1 / h_{oe})}) / R_L × 100\% = (2200 - 2041.86) / 2200 × 100\% = 7.19\%\).

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Most popular questions from this chapter

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.

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. \(A_{v}=V_{o} / V_{i}\)

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 \(3.8 \mathrm{~mA}\) ?

a. Sketch the Giacoletto (hybrid \(\pi\) ) model for a common-emitter transistor if \(r_{b}=4 \Omega\), \(C_{m}=5 \mathrm{pF}, C_{u}=1.5 \mathrm{pF}, h_{o e}=18 \mu \mathrm{S}, \beta=120\), and \(r_{e}=14 .\) b. If the applied load is \(1.2 \mathrm{k} \Omega\) and the source resistance is \(250 \Omega\), draw the approximate hybrid \(\pi\) model for the low- and mid- frequency range.
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