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 Es cos(ωt + φ) to the phase detector with transitions at the
zeros of sinωt, i.e. at t = 0, π/ω, 2π/ω etc. Let us further assume that we average the
output, Vout, by passing it through a low-pass filter whose time constant is longer than
one period:
τ = RC >> T = 2π/ω
Then the low pass filter output is
!
Escos(
"
t+
#
) |0
$
/
"
%Escos(
"
t+
#
) |
$
/
"
2
$
/
"
where the brackets represent averages, and the minus sign comes from the gain reversal
over alternate half cycles of Vref.
Show that
!
Vout ="(2Es/
#
)sin
$
by doing the integrals and assuming unity gain for the amplifier
