Question 11.5: An amplifier has a voltage gain of 15 dB. If the input signa...

Voltage gain in         dB = 20 \log_{10}  V_{2}/V_{1}

Therefore,                  15 = 20 \log_{10}  V_{2}/V_{1}

15/20 = \log_{10}  V_{2}/V_{1}

0.75 = \log_{10}  V_{2}/0.8

Taking antilogarithm, we get

10^{0.75} = V_{2}/0.8

Hence,                            V_{2} = 10^{0.75} × 0.8 = 4.5  V

In amplifier analysis, half power gain is found out as follows:

Half power gain in dB = 10 \log_{10} \frac{P_{out put  max} /2}{P_{out put  max}}

= 10 \log_{10}(\frac{1}{2} )

= 10 \log_{10} (0.5)

= – 3 dB

Hence, the half power gain is maximum gain minus three decibels.

As shown in Fig. 11.4, half power bandwidth i.e., (f_2 \sim f_1), is the frequency range over which gain is more than half power gain.