Two messages, one wire. Each in its own band.
Ten minutes of reading. Move the sliders, then Figure 1 of the manual will make sense block by block.
Many messages, one channel
Two audio messages both live between a few hundred hertz and a few kilohertz. Put them on one wire as they are and they mix for good: no filter can pull them apart, because they use the same frequencies. Frequency division multiplexing (FDM) first moves each message to its own band with a modulator and its own carrier, then adds the shifted signals. In the frequency domain they now sit side by side, so at the far end a band pass filter can pick out one band, and a demodulator can bring that message back down to audio.
Every message keeps the channel all the time, but only a slice of its frequencies. (Time division multiplexing does the opposite: every message gets all the frequencies, but only a slice of the time.) The IR-4104 does this for two channels with double sideband modulation.
DSB in the balanced modulator
A balanced modulator multiplies the audio by the carrier. For a tone m(t) = A cos 2πfmt the product splits into two tones: A/2 cos 2π(fc − fm)t and A/2 cos 2π(fc + fm)t, the lower and upper sidebands. The carrier itself is balanced out, so this is DSB with suppressed carrier (DSB SC): the AM O/P of the trainer carries no power at fc, only the two sidebands.
In time the envelope follows the size of the audio, not the audio itself: it touches zero every time the audio crosses zero, and there the carrier flips by 180°. That is why a plain envelope detector (Lab 6) cannot recover DSB SC, and the receiver needs a copy of the carrier.
Channels side by side: bandwidth and guard band
A DSB channel with a message up to fm occupies fc − fm to fc + fm: a bandwidth of 2 fm. The carriers must be far enough apart that the channels never overlap, and a little more, because a real band pass filter does not drop from full gain to nothing at one frequency. The empty gap left between the top of one channel and the bottom of the next is the guard band.
On the IR-4104 the carriers are 25 kHz and 55 kHz, the audio generators reach 4 kHz, and each band pass filter is centred on its carrier with a pass band of about ±6 kHz. Move carrier 2 down in the demo until the channels touch: filter 1 then lets part of channel 2 through, and the channels can no longer be separated.
Getting one channel back: filter, then product detector
The band pass filter of each receiver section passes its own channel and stops the other. The DSB demodulator is a second multiplier, fed with the same carrier as the modulator (a product or coherent detector). The equations are below.
The message comes back multiplied by cos φ. In phase (φ = 0) it is full size; at φ = 90° it disappears completely. A carrier of the wrong frequency is worse: the product lands somewhere above the audio band and the low pass filter removes everything. On the trainer the receiver carriers are copies of the transmitter oscillators, and the Carrier knob of each demodulator turns the phase.
The AC amplifier and the low pass filter
The demodulator output is the audio plus a strong component around twice the carrier (50 kHz for channel 1), and a small DC level from the bit of carrier the balanced modulator leaks. The AC amplifier blocks the DC and lets you trim the level with its Gain Adjust preset. The low pass filter (5 kHz, fourth order on the trainer) removes the double frequency part, so only the message is left. Its gain at the top of the audio range is 0.93, so a 4 kHz message comes out a little smaller.
On the bench (manual Figure 1)
Set the two audio generators first (about 1 kHz and 2 kHz, so the channels are easy to tell apart), and measure each carrier on CH2 at 20 µs/div or faster. Wire the transmitter, look at AM O/P and at the summing amplifier output, then wire both receiver sections. Compare each Low Pass Filter O/P with its own generator on CH1 at about 500 µs/div. The spectrum analyzer on the Summing O/P with the 50 kHz preset shows both channels at once.
What you should see
| Point (messages 1 kHz and 2 kHz, 1 V p-p; carriers 2 V p-p) | Scope | Spectrum analyzer |
|---|---|---|
| Carrier 1 O/P / Carrier 2 O/P | 2 V p-p sine, 25 kHz / 55 kHz | one line each |
| Balanced Modulator 1 AM O/P | DSB: 1 V p-p envelope, phase flips where the audio crosses zero | 24 and 26 kHz at about −2 dBm, the leaked carrier nearly 30 dB lower |
| Summing Amplifier O/P | both DSB signals added, hard to read | four lines: 24, 26, 53, 57 kHz, guard band 27 kHz |
| Band Pass Filter 1 O/P | channel 1 only | channel 2 about 40 dB down |
| DSB Demodulator 1 Audio O/P | 1 kHz audio with a 50 kHz ripple on it | 1 kHz plus lines near 50 kHz |
| Low Pass Filter 1 / 2 O/P | clean 1 kHz / 2 kHz, about 1 V p-p, same shape as the message | one audio line |
| Demodulator Carrier knob at either end | local carrier 90° out of phase: the recovered message almost vanishes | |
| Carrier 2 fed to Demodulator 1 | nothing at the Low Pass Filter 1 O/P | |
Values are those of the simulator model of the IR-4104. A real trainer differs a little from unit to unit; the way each block changes the signal is the same.
Where FDM is used
Every AM and FM station has its own carrier. The air is the shared channel and the tuner of your receiver is the band pass filter.
Long distance trunks once stacked 12 voice channels of 4 kHz into one 60 to 108 kHz group, and groups into supergroups, all by FDM with SSB.
Wi-Fi, 4G and 5G use OFDM: hundreds of closely packed sub-carriers that overlap without interfering, demultiplexed with an FFT.
Wavelength division multiplexing is FDM with light: each channel is a different colour, and one fibre can carry more than a hundred.
Check yourself
Q1What do you mean by FDM?
Frequency division multiplexing sends several messages over one channel at the same time by giving each message its own band of frequencies. Each message modulates its own carrier, the modulated signals are added, and at the receiver band pass filters separate the bands before each one is demodulated.
Q2Briefly describe the term modulation.
Modulation is changing a property of a high frequency carrier (its amplitude, frequency or phase) in step with the message. It moves the information of the message to the frequencies around the carrier.
Q3Why is it necessary to modulate analog signals?
To move the message to a band that suits the channel: antennas of practical size need high frequencies, and many messages can share one channel only if each is moved to a different band (FDM). Modulation also lets the receiver select one signal, and some types (FM) trade bandwidth for better noise performance.
Q4Give the types of modulation.
Analog: amplitude modulation (AM, DSB SC, SSB, VSB), frequency modulation and phase modulation. Pulse: PAM, PWM, PPM and PCM. Digital carrier modulation: ASK, FSK, PSK and QAM.
Q5What is amplitude modulation?
The amplitude of the carrier is changed in step with the message: s(t) = Ac[1 + μ m(t)] cos 2πfct. Its spectrum has the carrier and two sidebands at fc ± fm, and the envelope of the wave follows the message. With the carrier removed it becomes DSB SC, which the IR-4104 uses.
Q6Why is the output of the balanced modulator called DSB SC?
Because it contains the two sidebands fc − fm and fc + fm but (almost) no carrier: the balanced circuit cancels the carrier, which carries no information. On the analyzer you see two lines and only a very small leak at fc.
Q7What is a guard band and why is it needed?
It is the empty gap between neighbouring channels. Filters cannot go from full pass to full stop at one frequency, so without a gap part of the neighbouring channel would get through the band pass filter and appear as crosstalk.
Q8Why must the demodulator use the same carrier as the modulator, in phase?
The product detector output follows m(t) cos φ (the multiplier gives ½ m(t) cos φ and the detector gain makes up the ½), where φ is the phase difference between the local carrier and the one used at the transmitter. At 90° the message disappears. A carrier of another frequency moves the channel to some other band, not to audio, and the low pass filter removes it.
Q9What does the low pass filter after the demodulator remove?
The product of the channel and the carrier also contains a component around twice the carrier frequency, and some leakage. The low pass filter passes the audio band only, so the output is a clean copy of the message.