AM Demodulation peak detect Demodulation is about recovering the original signal Crystal Radio Example Antenna Long Wire FM AM A simple Diode Tuning Circuit Demodulation Circuit envelop of AM Signal Filter Mechanical Basically a tapped Inductor L and variable Capacitor C We ll not spend a lot of time on the AM crystal radio although I love it dearly as a COOL ultra minimal piece of electronics Imagine you get radio FREE with no batteries required But The things we will look at and actually do a bit in lab is to consider the peak detector I e the means for demodulating the AM signal From a block diagram point of view the circuit has a tuning component frequency selective filter attached to the antenna basically a wire for the basic X tal radio The demodulation consists of a diode called the crystal from the good old days of Empire of the Air movie we ll watch and an R C filter to get rid of the carrier frequency In the Radio Shack version there is no C needed your ear bones can t respond to the carrier so they act as the filter The following slide gives a more electronics oriented view of the circuit 1 Signal Flow in Crystal Radio Circuit Level Issues V Wire Antenna V time BW fo Filter fo set by LC BW set by RLC music tuning ground 0V KX KY KZ frequency time V only So here s the incoming modulated signal and the parallel L C so called tank circuit that is hopefully selective enough having a high enough Q a term that you ll soon come to know and love that tunes the radio to the desired frequency Selective enough means that you receive KX and don t also get KY and KZ for AM you definitely won t get KZSU The diode rectified signal looks as shown basically we keep the positive side of the signals referenced to GROUND Comment about X tal Radios To get a good signal you do indeed need a solid ground an interesting challenge unto itself Back to the detection Now our challenge is to keep the envelop and get rid of the carrier basically to filter it out Per the NEW EE101A diodes are used to create power supplies a lab experience now in progress Here we are using the incoming AM signal to create a power supply I e no battery needed where the ripple is the information music etc that we want to hear 2 About Peak Detection and Waveforms d dt i d o dt Generally we want d dt o d i dt So let s look at a cycle of the music that rides on top of the much higher frequency carrier By analogy to the power supply example we will use an R C filter to decay at a rate that hopefully follows the modulated signal but doesn t decay too fast and therefore follow the carrier This plot shows us that the modulated signal has a slope and the result of the R C filter will also have a slope Generally speaking we want the slope of the filtering to be steeper than the envelope If it is NOT steeper we re not following the modulating signal the very last slide in this set corresponds to Diagonal Clipping the consequence of going too slowly If it s TOO STEEP we re not filtering out the carrier OK Let s try and put that in a more formal mathematical form 3 Condition for Optimum RC Incoming Signal Req Vo t R What happens peak to peak after diode C refresh needed from next phase pulse via diode 1 T c T m RC m 1 1 1 2 m Here we define the circuit to be considered and used in lab a bit more formally We have the diode that gets us half wave rectification Going from one carrier peak to the next we have an RC fall off as shown At the end of the following few pages we will determine an optimum C value in terms of R m and m This figure simply is showing graphically both the circuit RC in relationship to the carrier period and also how that compares to the period of the modulating signal The BOXED equation tells us the final result in terms of how the RC and modulation index should ultimately relate to the modulating frequency Now let s take a very quick stroll through the derivation of the real inequality that is involved 4 About the Equation for optimum v i Vi 1 m cos m t v o Ve t Generally want Given that we we want T RC d dt o d i dt t V T RC e Vi m m sin m t TRC equating v i v o at some t This is THE constraint 1 m cos m t m m sin m t equation now let s TRC make it useful Assume that the incoming envelop waveform looks as shown above first equation The R C circuit will have a response that looks like that shown in the second equation Taking the derivative of both equations with respect to time and applying the desired inequality per the previous slide the third equation is obtained Also at some point in time the top two equations can be equated and that result combined with the third equation gives the fourth equation an inequality that relates RC time constant TRC Modulation index m Modulation frequency m Unfortunately how to work with this equation is NOT so easy and another page of equation hacking is needed We won t spend much time on the hacking but we need to get to the final result 5 And the answer is after some trig manipulations 1 2 2 1 m m TRC m where TRC RC then 1 2 2 1 m C m 1 1 2 1 m mR mR The KEY equation for C in terms of m m R There are some trigonometric identities that allow us to simplify the inequality from the previous page to the one shown here The RC time constant is defined as shown The bracked boxed equation tells us how small to make C in the RC in terms of m m and R If C is larger then we start to loose information in the envelop due to diagonal clipping If C is too small I e why not make it ZERO then we certainly follow the envelop but we are NOT getting rid of the carrier Basically if C is too small we ve kept too much and we haven t really demodulated the signal 6 What we DON T want Clipping Diagonal Clipping V envelope e t t 0 t Considering the dark side what we DON T want If the slopes in the above inequality are reversed here s what it looks like Basically if the RC time constant is too long then as the modulated signal decreases the sampled point shown simply falls off and ignores the stuff below it This is called Diagonal …