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Chapter 20: Problem 62

In a common base transistor \(i_{c}=19 i_{b}\), load and plate resistance are \(4 \mathrm{k} \Omega\) and \(1 \mathrm{k} \Omega\). The voltage gain of amplifier will be (A) 80 (B) \(4.2\) (C) \(3.8\) (D) 76

Short Answer

Expert verified
The voltage gain (AV) of an amplifier can be calculated through the ratio of the output voltage (\(V_o\)) and input voltage (\(V_i\)). We find the output and input voltages by applying Ohm's law on the given load resistance (\(R_L = 4k\Omega\)) and plate resistance (\(R_p = 1k\Omega\)). Hence, the output voltage is \(V_o = I_c 脳 R_L\), and the input voltage is \(V_i = I_b 脳 R_p\). Given the relationship \(i_c = 19i_b\), we substitute these values into the voltage gain formula to give: \(A_V = \frac{19I_b 脳 4k\Omega}{I_b 脳 1k\Omega}\). Simplifying this, the voltage gain is 76, which corresponds to option (D).

Step by step solution

01

Recall the formula for voltage gain

The voltage gain (AV) of an amplifier can be calculated using the following formula: \[A_V = \frac{V_o}{V_i}\] Where \(V_o\) is the output voltage and \(V_i\) is the input voltage.
02

Find the output voltage

The output voltage across the load resistance can be found by using Ohm's law, which states that the voltage is equal to the product of the current and the resistance: \[V_o = I_c 脳 R_L\] Where \(I_c\) is the collector current and \(R_L\) is the load resistance.
03

Find the input voltage

The input voltage can be found using Ohm's law as well, but in this case, it will be defined in terms of base current and plate resistance: \[V_i = I_b 脳 R_p\] Where \(I_b\) is the base current and \(R_p\) is the plate resistance.
04

Substitute given values in the formula

We know that \(i_c = 19i_b\), and we are given the load resistance (\(R_L = 4k\Omega\)) and plate resistance (\(R_p = 1k\Omega\)). We can use these values to rewrite the formula for voltage gain: \[A_V = \frac{19I_b 脳 4k\Omega}{I_b 脳 1k\Omega}\]
05

Simplify and solve for voltage gain

Now, we can simplify and solve the expression for the voltage gain: \[A_V = \frac{19I_b 脳 4k\Omega}{I_b 脳 1k\Omega} = \frac{19 脳 4}{1} = 76\] The voltage gain of the amplifier is 76, which corresponds to option (D).

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