This article will look primarily at the methods used for modulation and demodulation of radio messages.
Looking back at previous articles, one might wonder how all of this relates to the original point of figuring out how to get a signal from point A to point B. Without going into a ton of detail regarding antenna design, we’d have to have a massive antenna to broadcast at anything approaching 60Hz. I’m talking hundreds or thousands of miles of cabling. There are some innovative ways to do it using deep drilled cabling in the Earth but that’s far out of reach for your average radio station. Even something as high as 10KHz would require an antenna that’s about 17 miles long. Instead, we modulate our communications signals to very high frequencies so that our antennas can be more easily constructed.
How do we modulate our messages?
It just so happens that one of the simpler methods of modulation is one of our oldest. Amplitude modulation is where the amplitude of our message is varied in order to modulate it to a higher frequency. Normally a message is modulated using a much higher frequency signal. There are several ways this can be accomplished.
Double sideband-suppressed carrier (DSB-SC)
This method uses only the upper and lower sidebands of the signal in order to pass a message. The carrier signal is suppressed which results in a substantial power savings. However, in doing so, our bandwidth requirement is still relatively high. This is accomplished by utilizing a product modulator circuit to multiply our message signal by the carrier signal.
One of the most common forms of product modulators used is the ring modulator (also known as a double-balanced modulator). This is simply a collection of diodes that are switched at a certain frequency in order to inject the carrier wave into the message. This is a similar process to electromechanical commutation.
For DSB-SC modulation, we use the following two equations for time and frequency domain representation.
S(t) = m(t) Ac cos(2pi fc t)
S(f) = ½ Ac [M(f-fc)+M(f+fc) where M is the shifted message convolved with each Fourier-domain Dirac-delta impulse, Ac is the amplitude of the carrier wave, and fc is the frequency of the carrier wave. The higher frequency component is known as the upper sideband whereas the lower frequency component is known as the lower sideband. The two should be symmetric. If the message signal occurs at more than one frequency, that will result in multiple frequencies in each sideband.
One problem associated with DSB-SC modulation is the phase reversal that occurs to the message signal when the carrier signal waveform has a zero crossing at the half-cycle point. This causes the demodulation process to be slightly more complex to account for the phase reversal without losing message integrity.
In order to demodulate a DSB-SC signal, another product modulator acting at the original carrier frequency must be used. This is combined with a low-pass filter to obtain the original message from the output of the product modulator.
Since the original carrier frequency may not be known, use of synchronization circuitry is required. One solution to this is the phase lock loop. The phase lock loop is composed of a product modulator, low pass filter, and voltage controlled oscillator. The voltage controlled oscillator acts as a sinusoidal generator where the output is determined by the voltage applied to the input. The VCO output is adjusted such that with a zero input signal, the output signal is 90 degrees out of phase with the detected carrier signal. This is accomplished by isolating the carrier signal with a band pass filter and feeding it back into the phase lock loop as a pilot signal. If isolation of the carrier signal isn’t possible, it is possible to use a Costas loop instead. This uses a phase discriminator to approximate the carrier signal.
Double sideband-large carrier (DSB-LC)
This is the standard broadcast AM that we’re all used to. DSB-LC modulation works by adding a DC offset to our message signal prior to performing DSB-SC modulation. This results in the carrier signal showing up in the final signal waveform. This results in an “enveloping” effect.
s(t) = Ac[1+u*cos(2 pi fm t) cos (2 pi fc t) where u is the modulation index found by multiplying the amplitude of the message signal times the amplitude sensitivity. This amplitude sensitivity is chosen based on the scaling of the original DSB-SC signal compared to the carrier envelope that it is placed within. u can also be calculated by the equation u = (max amplitude – min amplitude) / (max amplitude + minimum amplitude).
The benefit of this modulation method is that phase reversals only occur during over-modulation conditions which simplifies the demodulation process. The primary downside of this modulation scheme is that the majority of the signal power is wasted in the carrier signal. This requires extra amplification during demodulation.
Demodulation can be accomplished using the synchronous detection techniques discussed for DSB-SC; however, a simpler method exists called “envelope detection.” This can take the form of a half-wave rectifier with a parallel RC circuit filter. On positive half-cycles, the capacitor will be charger. As the signal falls off, the diode will block the signal and allow the capacitor to slowly discharge through the resistor until the next peak event. This will act to “smooth” the waveform out until only the original message signal remains. If necessary, a series capacitor/buffering circuit can be used to remove the DC offset and obtain the exact message signal.
Single sideband (SSB) modulation
Single sideband modulation is where the modulated wave only has only the upper or the lower sideband. This is especially well suited to voice signal transmission as the frequency content of the human voice has a large energy gap between 0 and 200Hz. This method of modulation requires the lowest amount of power and bandwidth; however, it also has a relatively high complexity associated with modulation and demodulation.
The theoretically easiest way to create a SSB modulated signal is to create a DSB-SC signal then suppress one sideband by filtering it out. However, this requires an extremely accurate filter which may be prohibitive. Realistically, it is easier to construct a circuit that duplicates the DSB-SC signal and phase shifts it by 90 degrees. It is then combined with the original signal to cancel one sideband completely. The downside to this method is that the circuit will only work for a small bandwidth of signals without being reconfigured.
Vestigial sideband (VSB) modulation
This method of modulation uses one single sideband to transmit a message. This is useful mainly for transmitting television signals due to the wideband nature of the signal.
This method of modulation consumes less bandwidth compared to DSB-LC while still allowing for the use of an envelope detector for demodulation.
In order to create a VSB signal, the same method of producing a DSB-SC signal is followed with one exception: a sideband shaping filter. This allows the inner or outer sidebands to be reduced in amplitude which causes a corresponding reduction in bandwidth requirements. As a result, bandwidth intense applications can be made to fit in a smaller frequency range.