Week 9: Alternating Current Circuits 333
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RV(t) sin( t)ωodiode (crystal)Figure 135: A very simple, idealized crystal radio circuit using a variable capacitor instead of variable
inductance (or variable both). Note also the presence of adiode decoder– a one-way gate for current
(which flows only in the direction of the “arrow”).
ris amixof the physical resistance of the antenna wire and its “radiation resistance” and is the
quantity that needs to be impedance matched (more or less) by theloadRfor maximum power
delivery at resonance. Recall that providing an easy (low impedance) path to ground through
eitherLorCfor a given frequency will effectively short out the antenna so thatall its power at
that frequency will be dissipated in the antenna, not inR. Only whenLChasinfinitecollective
impedance at resonance will the power delivery be balanced inrand (matched)R.
This simple parallel signalalonewould suffice to tune in the AM carrier, but if we listened to the
headphoneswithoutthe diode decoder visible in the circuit, we’d hear –nothing!That’s because the
carrier is at a very high frequency (typically over 500 kHz) that is well above the range of human
hearing. We have toremovethe carrier, leaving the signal.
Diodes act as a one-way gate for the voltage, allowing current to flow only in the direction of
the “arrow” in the diode. This process is called “rectification” (literally right-sidification), and a
single diode is ahalf-wave rectifier, cutting off of thenegativeparts of the current and passing
only the positive “right side up” voltage/current variation. Placing asmall capacitor in the line
containing the headphones (usually not necessary, as the diode and the headphones together have
some capacitance) removes the DC bias and “smears” out the top-half carrier waves to fill in a good
approximation to the original signal.
The original diodes werecrystalsof e.g. lead galena in a mount with an adjustable wire whisker
in contact with the crystal – hence “crystal radio”. The wire whisker created a semiconducting
interface with the crystal that in turn only passed current in one direction (with a very high back
resistance that effectively prevented it in the other). However, lots of other conductor interfaces will
provide the same effect, including a graphite pencil (basis of so-called “foxhole radios” used by GIs
in World War II, usually built out of surplus junk scavenged on a battlefield).
Of course using a single diode in a circuit wasteshalf of the powerpicked up by the incoming
antenna! It is much better to usefourdiodes turned into afull-wave rectifier. Look over the
following circuit in figure 136 (intended to replace the entire diode/headphone arrangement in the
circuit above) and understand how as thevoltageoscillates positive to negative, thecurrentthrough
the headphones only passes in just one direction.
This arrangement basicallyflipsthe negative half-waves and fills them into the “holes” between
the positive ones, recovering the full energy. Again, when smeared out a bit by anRCtime constant
by the capacitance of the headphones, this accurately reconstructs the decoded AM signal, without
any bias, with a bit of high frequency “ripple” that the human ear cannot hear. A schematic of the