From the July '82 issue of "Popular Electronics" In the something different department: Here's an early simplified shot at explaining Sync Detectors AM Synchronous Detection (Simplistically but you need to know a little algebra/trig) ----------------------------------------------------------- If I were to receive an unmodulated RF carrier waveform on the antenna of my receiver, I would filter out other unwanted signals and amplify the desired received carrier and its voltage could be expressed mathematically as a function of time as: c(t) = A1 * sin(2*PI*Fc*t) A1 is a constant (amplitude). 2 * PI is a constant, Fc is how many full cycles of oscillation the carrier manifests per second. t is good old-fashioned time. If the sender were to modulate the signal, they would esentially multiply it by a modulating voltage which is also a function of time say, m(t). The voltage seen at the output of a microphone into which someone is speaking is a time-varying signal. The amplitude modulation that is employed for classic AM broadcast band and many shortwave radios is especially suited to simple diode detectors which, among other approaches, can be described as "envelope detectors". This modulation scheme requires that the carrier never be multiplied by a negative number (that would invert the phase of the carrier during the negative excursions of the modulating signal). Further, in order to provide the best signal at the simpler demodulators, the modulation signal is normalized to have a minimum value of 0.0 and a maximum value of 1.0. It's quiescent value (silence into the microphone) would be 0.5. So after all that, our modulated transmitted program voltage is: p(t) = m(t) * A1 * sin(2*PI*Fc*t) or p(t) = A1 * m(t) * sin(2*PI*Fc*t) Great, now after we receive, filter, and amplify our desired signal let's (somehow) build an oscillator that can produce a waveform just like our carrier (exact same frequency) except that it has constant amplitude and it is delayed by a quarter of a cycle (i.e. 90 degrees or PI/2 radians). This local signal would be described by: l(t) = A2 * sin(2*PI*Fc*t - PI/2) because PI radians = 360 degrees. Now let's multiply the modulated, amplitude varying received signal, p(t) by this local carrier signal, l(t): l(t) * p(t) = A2 * sin(2*PI*Fc*t - PI/2) * m(t) * A1 * sin(2*PI*Fc*t) or l(t) * p(t) = A1 * A2 * m(t) * sin(2*PI*Fc*t - PI/2) * sin(2*PI*Fc*t) or l(t) * p(t) = k * m(t) * sin(A) * sin(A) where k = A1 * A2, A = 2 * PI * Fc * t - PI/2, B = 2 * PI * Fc * t or A = B - PI/2 A quick glance at a trig/algebra/math book will restore the fact that: sin(A) * sin(B) = 0.5 * [ cos(A - B) - cos(A + B) ] = 0.5 * [ cos((B - PI/2) - B) - cos((B - PI/2) + B) = 0.5 * [ cos( -PI/2) - cos(2 * B - PI/2) ] NOTE: cos(-PI/2) = -1 And our locally multiplied signal is: l(t) * p(t) = k * m(t) [ -1 - cos(2 * B - PI/2] l(t) * p(t) = -(k * m(t)) - k * m(t) * cos(2 * B - PI/2). \____________ ___________/ V | This signal is at twice the frequency of the received carrier. This is easily filtered away. leaving l(t) * p(t) = -k * m(t) The negative sign means nothing to the receiver or listener as you can reverse the speaker leads in a radio and it has effect. m(t) is the original modulating signal scaled by k. Again, we don't care about k; we can turn the receiver volume control up or down. So we have what we're after, m(t)! So to build a synchronous detector one might: -------------------------------------------- 1.) Receive, filter and amplify the desired signal. 2.) Somehow, make a constant amplitude sinewave with exactly the same frequency as the carrier of the received signal but delayed exactly 1/4 of a cycle. 3.) Multiply the local derived and delayed carrier by the received signal (this can be done with circuits similar to those used in modulators). 4.) Filter off any energy at twice the received carrier frequency. 5.) The resulting signal is the modulating program signal.