For a multiplier with one signal input having a peak voltage of 5 mV and a frequency 1200 kHz and the other input having a peak voltage of 10 mV and a frequency of 1655 kHz, the output expression for this multiplier is: 

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  1. 25 μV cos 2π (455 kHz) t + 50 mV cos 2π (455 kHz) t
  2. 25 μV cos 2π (455 kHz) t - 25 μV cos 2π (2855 kHz) t
  3. 50 mV cos 2π (2855 kHz) t + 50 mV cos 2π (455 kHz) t
  4. 15 mV cos 2π (455 kHz) t + 15 mV cos 2π (2855 kHz) t

Answer (Detailed Solution Below)

Option 4 : 15 mV cos 2π (455 kHz) t + 15 mV cos 2π (2855 kHz) t
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Detailed Solution

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Analog multiplier circuit

In electronics, an analog multiplier is a device that takes two analog signals and produces an equivalent output.

The output voltage of the multiplier circuit is:

\(V=V_1+V_2\)

The output frequency is:

\(f=f_1-f_2\) and \(f=f_1+f_2\)

Calculation

Given, V1 = 10 mV at f1 = 1655 kHz

V2 = 5 mV at f2 = 1200 kHz

\(V=10+5=15\space mV\)

\(f=f_1-f_2\)

\(f=1655-1200=455 \space kHz\)

\(f=f_1+f_2\)

\(f=1655+1200=2855 \space kHz\)

Hence, the output of the multiplier circuit is:

Vo = 15 mV cos 2π (455 kHz) t + 15 mV cos 2π (2855 kHz) t

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