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HH_15_2 - by passing it through a low-pass filter whose...

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Problem HH15.2 The figure below shows a basic phase detector. An analog signal passes through a linear amplifier whose gain is reversed by a square- wave “reference” signal controlling an FET switch. The output signal passes through a low-pass filter, RC. Let’s assume we apply a signal E s cos( ω t + φ ) to the phase detector with transitions at the zeros of sin ω t, i.e. at t = 0, π / ω , 2 π / ω etc. Let us further assume that we average the output, V out , by passing it through a low-pass filter whose time constant is longer than
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Unformatted text preview: , by passing it through a low-pass filter whose time constant is longer than one period: τ = RC >> T = 2 π / ω Then the low pass filter output is E s cos( " t + # ) | $ / % E s cos( t + ) | / 2 / where the brackets represent averages, and the minus sign comes from the gain reversal over alternate half cycles of V ref . Show that V out = " (2 E s / )sin by doing the integrals and assuming unity gain for the amplifier...
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