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where Vd is the forward bias voltage drop on the diode. If the 1 is ignored (which can be done for even small Vd's at room temperature) and the exp term expanded in a series of powers of Vd, then the diode curve can be approximated reasonably by an expression consisting of terms upto the square of Vd. So this square law expression represents th diode current. Now when Vd is a modulated signal, this square term would produce the sum and difference of the carrier and the signal frequencies. The carrier can be filtered out giving the signal.
Thus since we use the square term explicitly to detect a signal, the diode is sometimes called the square law detector.
I am a bit confuse about this sentence
"Now when Vd is a modulated signal, this square term would produce the sum and difference of the carrier and the signal frequencies "
Suppose the Vd across the diode consists of the sum of a AM modulated signal and a frequency same as the carrier, due to the square term the current will have harmonics and intermodulation products, one of which will be the demodulated AM signal.
IT is evident from voltage-current characteristics . it is not a st.line but a parabolic nature.the eqn of parabola is a second degree eqn.similarly for this also.
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