Question 14.3: An amplifier has a voltage gain of 10, an infinite input res......
An amplifier has a voltage gain of 10, an infinite input resistance and zero output resistance. The amplifier is connected, as in Example 14.1, to a sensor that produces a voltage of 2 V and has an output resistance of 100 Ω, and to a load resistance of 50 Ω. What will be the output voltage of the amplifier?
Step-by-Step
As before, we first draw an equivalent circuit of the amplifier, sensor and load.
From the diagram
V_{i} = \frac{R_{i}}{R_{s} + R_{i}} V_{s}When R_{i} is much larger than R_{s} , this approximates to
V_{i} = \frac{R_{i}}{R_{s} + R_{i}} V_{s} ≈ \frac{R_{i}}{R_{i}} V_{s}In this case, R_{i} is infinite, so we can say
V_{i} = \frac{R_{i}}{R_{i}} V_{s} = V_{s} = 2 Vand, therefore, the output voltage is given by
V_{0} = A_{v} V_{i} \frac{R_{L}}{R_{0} + R_{L}} = 10 V_{i} \frac {50 Ω}{0 + 50 Ω} = 10 V_{i} = 10×2 = 20 VThe arrangement now has a voltage gain of 10 and there are no loading effects.
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