## Amplitude Modulation and Superheterodynes

The balanced modulator, superheterodynes, the autodyne converter, automatic gain control, amplitude and frequency modulation, and function generator chips

### Modulation

We briefly encountered the balanced modulator as a phase detector for phase-locked loops. This circuit is worth further attention, since it performs the interesting duty of multiplying two signals. Also, the ingenuity of amplitude modulation deserves a look. A good balanced modulator is the LM1496, whose circuit is shown below. This circuit comes in a 14-pin DIP, and the pin numbers are given in the diagram. The 500Ω resistors are internal; the other components, 10 resistors and two capacitors, are attached externally. What we have here are two differential amplifiers made from Q1-Q4 and fed in antiphase by one input, which we shall call the carrier, normally the input of higher frequency ω1. The total currents for these differential amplifiers are supplied by a differential amplifier made from Q5 and Q6, and fed by the signal or modulation frequency ω2. We know that the gain of a differential amplifier is proportional to its current, so the lower amplifier controls the gain of the upper amplifiers, which will be proportional to the signal input. The 1k resistor between pins 2 and 3 joins the bases of Q5 and Q6, and so determines the gain of this amplifier. Q7-Q9 are the current sources for the amplifiers. The bias current in Q7, which is determined mainly by the resistor from pin 5 to ground, is mirrored by Q8 and Q9. In this circuit, the bias current has been set at close to 1.0 mA. Note that there is a V- pin, but no V+ pin. The collectors of Q1-Q4 are pulled up to +V by external resistors, here 3.9k. The upper amplifiers are biased to a suitable level (6.0 V) by the external voltage divider made up of 1k resistors, bypassed to ground. The bases are connected to the bias voltage through 51Ω resistors, across which the input is impressed. You could just as easily use 47Ω and 4.7k resistors as the ones shown. The bases of the lower amplifier are connected to ground by 51Ω resistors in the same way.

There are inverting and noninverting inputs for both carrier and signal, which can be fed differentially or single-ended. The single-ended feed is more convenient here. The carrier is put into the + carrier input through an 0.1 coupling capacitor, while the signal can be supplied directly to the + signal input, if it swings about ground, perhaps with a small DC component. When the circuit is properly arranged, the voltage at pins 6 and 12 should be about 8 V. The output can be taken from these pins, again either differentially or single-ended. The LM1496 can stand input voltages of up to 5 V, and the inputs should not be more than 5 V apart (to avoid breaking down the emitter junctions).

For the carrier, I used an RF signal generator supplying a carrier of about 500 kHz. It could give only 0.72 V peak to peak against the 51Ω resistors, but this was enough. Of course, a function generator would work as well if you have no signal generator. If you have only one function generator, use an oscillator package to get a carrier frequency. The signal was supplied by the function generator, at 10 kHz. Both frequencies could easily be varied, but these values were conveninent. Watch the output on the scope, as well as the signal input, while you increase the signal amplitude slowly. 0.2 V peak to peak at the input was satisfactory. (the 600Ω output impedance has to overcome the 51Ω at the inputs. This low resistance does help protect the inputs, but if it is too restrictive, try 100Ω or so instead).

The scope display of the output is pretty, but it is even prettier when you understand what is going on. If the carrier is cos(ω1t) and the signal is A cos(ω2t) - B, then the output is A cos(ω1t)cos(ω2t) - B cos(ω1t) = (A/2)cos[(ω1 + ω2)t] + B cos(ω1t) + (A/2)cos[(ω1 - ω2)t]. We can vary A and B by adjusting the amplitude and DC offset of the function generator. The result, in general, is the sum of three waves, one at the carrier frequency, and two sidebands at the sum and difference frequencies. Information can be carried in the difference of the sideband frequencies. The carrier does not carry any information in itself. See what happens as you vary B (the DC bias in the signal). An AM signal is often represented by E(1 + m sin ωm)sin ωc, where subscripts m and c refer to modulation and carrier, and m is the degree of modulation.

When B = 0, you have only the sidebands. Such a signal is called Double Sideband, Suppressed Carrier or DSSC. The output looks like beating waves, which indeed it is, and the beat frequency is twice the signal frequency. Now carefully adjust B until B = A/2. The envelope of the output will exactly reproduce the signal, with the amplitude of the carrier varying sinusoidally. This is an amplitude-modulated (AM) wave, the type used in radio broadcasting. Although the added carrier carries no information, it plays an important function here, since the form of the wave is such that a rectified version will exactly reproduce the signal, after filtering out the carrier frequency. This means that detection, or recovery of the modulating signal, is extremely easy, and can be done with a simple diode (as in a crystal set!).

When the output signal has a minimum amplitude of zero, it's called 100% modulation. If you vary the signal amplitude (leaving the DC bias constant) you can see smaller percentages, down to 0%, which is plain carrier. If the signal is too large, you get overmodulation. Modulation percent is given by (max - min)/(max + min) x 100%.

### Detection

The recovery of the modulation from the AM wave is called detection. It should be clear that there is no modulation frequency in the RF wave, and no kind of filtering would produce it. Some nonlinear process is necessary to recreate the modulation frequencies. There are two general types of detectors, square-law and linear. A square-law detector has a transfer characteristic with a quadratic term: i = co + c1e + c2e2 + ..., where i might be collector current, and e base voltage. It is not necessary that only the quadratic term be present or even dominant; its presence is enough to ensure that modulation-frequency terms appear in i and can be filtered out. A transistor square-law detector is shown at the left. It is biased to operate at a low quiescent collector current (95 μA) so the output will be significantly nonlinear. I fed the base with a 550 kHz RF signal about 30% modulated with 1 kHz, which my RF signal generator produces. You can also use the signal from the LM1496 modulator you have built. The peak-to-peak amplitude of my signal was about 50 mV. The audio signal at the collector was about 1.3 V peak-to-peak, so the gain was about 36 dB. A square-law detector like this makes use of the amplification inherent in the device to produce a large output with a small input signal. The price that is paid for this is the existence of second-harmonic distortion if the degree of modulation is high. The fraction of distortion is m2/4. For 100% modulation, the second-harmonic distortion amounts to 25%. This is of no consequence for radiotelegraphy, but music suffers a bit.

Examine the waveforms at the collector with and without the .001 filter capacitor, and compare with the input waveform. Second-harmonic distortion is characterized by peaking of one loop and flattening of the other, so that the wave is no longer symmetrical about zero. A linear detector is simply a rectifier. It has no gain, but also no distortion. An example is easily made from two op-amps, as shown in the circuit on the right. The second op-amp is a precision half-wave rectifier (the second diode is to "catch" the op-amp on the other half-cycle and prevent it from saturating). Note that it eliminates the diode drop. The high frequency ripple is easily seen in the output, but the output does reproduce the modulating signal. Look at what happens for an overmodulated signal, and if you have an amplifier and loudspeaker, listen to it as well.

### The Superheterodyne

An AM radio receiver is fundamentally a very simple device. In its simplest form, a resonant circuit builds up a signal if there is one in space at the frequency to which it is tuned. A crystal (galena and cat-whisker) then rectifies the signal, which reproduces the modulation. All the energy comes from the received electromagnetic wave. A good receiver must combine sensitivity and selectivity. Sensitivity is obtained by amplification in several stages, while selectivity is obtained by a narrow bandwidth of the amplifiers. There is a severe problem if the receiver must tune over a reasonable interval, such as the medium-wave broadcast band from 550 kHz to 1.65 MHz. The filters of the several stages of amplification cannot track well enough as their frequency is varied if the bandwidth is narrow, so one must choose between sensitivity and selectivity in such a tuned-RF receiver. There are other problems as well, such as the variation in selectivity as the circuits are tuned over a wide range.

Armstrong solved the problem ingeniously by making the RF amplifiers fixed frequency. This frequency is called the intermediate frequency, or IF, and is 455 kHz in a typical broadcast receiver. (The IF in an FM receiver is usually 10.7 MHz, for the FM band of 88-108 MHz.) At the "front end" of the receiver is an oscillator, and the oscillator output is "mixed" with the received radio frequencies to produce the sum and difference frequencies (among others). Any nonlinear device can produce mixing; the basic operation is multiplication. The balanced modulator does this, for example. The sum or difference frequency that is the same as that to which the IF amplifiers are tuned is then amplified, all other frequencies being rejected. The beauty of this is that only the oscillator and the antenna tuned circuits have to be tuned; the IF amplifiers are fixed-frequency and can be made to have a narrow bandwidth. Finally, the IF signal is detected, usually with a simple half-wave linear diode detector, and the result fed to an audio amplifier. A receiver of this type is called a superheterodyne receiver, and most high-frequency receivers use the principle. A frequency-modulated signal must have a different kind of detector, of course, but otherwise the principle is the same.

I was lucky enough to find an "Elenco AM Radio Superhet 550" at a Radio Shack tent sale for \$2.00 that I fixed in 5 minutes. This is apparently a kit that someone built, and would be excellent practice in PC board stuffing, as well as an exellent demonstration of a superhet receiver, with everything laid out so you can see it, with test points and all. In most AM receivers today, all this is hidden inside an IC, and you can't get to it. It has a loopstick antenna (ferrite rod), oscillator and mixer, two IF stages (three 2N3904 transistors), and an LM386 audio amplifier with a 2" speaker, all operating from 9V. I also found a transformer for \$2.50 at the same tent sale, and have put together a 9 V, 240 mA power supply for the radio. It's a pretty good radio, too! The current drain at 9 V for a receiver like this is only 7-8 mA, suitable for the usual 9 V transistor radio battery.

### The Autodyne Converter An interesting circuit that contains much of interest is shown at the right, called an autodyne converter, which includes both mixer and oscillator. What it does is take a signal at frequency f from the antenna and mix it with an oscillator signal of frequency fo to produce a signal at a fixed frequency fif. When two frequencies are put into a linear circuit, only the same two frequencies are output. If the circuit is nonlinear, however, the output contains various differences and multiples of the input frequencies, a really mixed pot. We have seen how this happens in a rather clean case, that of the balanced modulator, which multiplies the two signals. Less clean mixing occurs when the signals are rectified, as by a diode, or even amplified by an amplifier with a nonlinear characteristic.

Radio waves passing by the antenna induce small voltages in it, and the resulting currents excite the LC circuit that is tuned to the frequency of the wave. A little of this energy is sent to the base of the transistor by inductive coupling, through a coupling capacitor that protects the DC bias on the base, provided by the voltage divider. The circuit is tuned by variable capacitor C1 to frequency f = 1/2πLC, where L is the associated inductance. Sometimes the antenna is a short rod of magnetic material, around which the coils are wound, called a loopstick, because it picks up the magnetic field of the wave like a loop antenna. Either way, a small signal at the frequency of the radio wave, f, is delivered to the base of the transistor.

On the other side is another tuned circuit with a variable capacitor C2, which is ganged with C1 so that they turn together. This circuit is tuned to the oscillator frequency fo, which is exactly 455 kHz higher in frequency than the desired radio wave frequency, so that the difference is always 455 kHz, the intermediate frequency. It is excited by the tickler coil in the collector lead of the transistor. The signal at a suitable low-impedance point (these air core transformers are very convenient in allowing good impedance matching) is put into the emitter through a coupling capacitor. We recall that both the base and emitter are possible inputs for amplifiers, common-emitter in the first, and common-base in the second. Here we are using both inputs to get both signals into the transistor. It is not essential that it be done this way, but simply convenient. The oscillator signal is much stronger than the signal from the antenna, which is desirable, since it means that the sidebands are converted along with the carrier without distortion.

A frequency 455 kHz on the other side of the oscillator frequency would also give a 455 kHz converted signal. This is called the image frequency. It does not have any effect, since the antenna tuned circuit easily rejects any signals so far away. The antenna tuned circuit does not need to be very selective, since the selectivity of the receiver is determined by the much narrower bandwidth of the IF amplifiers. The antenna tuned circuit has two duties: to build up signal voltage, and to reject image frequencies.

There is a third tuned circuit in the collector of the converter transistor, this time tuned to a fixed frequency, which is commonly 455 kHz for broadcast-band (540-1600 kHz; the frequency assignments are 10 kHz apart in the US) reception. The oscillator tunes from 995 to 2055 kHz, accordingly. The resistor and capacitor in the lead to VCC are there to decouple the stage from the power supply lead, to avoid unwanted feedback via this route. The tuned circuit is inductively coupled to the base of the first IF amplifier. All of the coils in this circuit come in small metal cans, with a tuning slug that allows them to be adjusted correctly. The tuned circuit presents a high impedance, and high gain, only to signals of frequency 455 kHz; other frequencies are not amplified, including the input and oscillator frequencies, which do not appear in the collector circuit.

If you have an Elenco 550 or some similar transistor radio where you can get to the required points, all this can be seen with an oscilloscope. The Elenco has all these things laid out with test points, but any receiver that uses discrete transistors will also do. The base of the converter transistor will show the modulated RF signal, the emitter will show the oscillator signal at fo, and the collector the converted signal at 455 kHz. Once again, the reason only 455 kHz voltage appears in the collector circuit is that the tuned circuit is tuned to this frequency. There is also oscillator current, but this is not seen by the voltage probe. I coupled the loopstick of the Elenco 550 to the signal generator with 9 turns of #22 wire wound in a coil, which was more than enough excitation. The carrier frequency was 1 MHz, with 1 kHz audio modulation. The base exhibited 0.2 V peak-to-peak at 1 MHz, and the emitter 0.2 V at the oscillator frequency of 1455 Hz. The emitter was not following the base; the oscillator frequency dominated. The collector showed 3.5 V peak-to-peak at 455 kHz, with the expected modulation envelope and a good deal of confusion at the limits of the signal. These signals should be examined both at low sweep speeds (1 ms/div) and high (1 μs/div) to know them well. The collector of the 1st IF showed a peak-to-peak signal of 0.8 V, of typical amplitude modulated form, and the 2nd IF 12 V amplitude (even outside the range of VCC!). The detected signal was quite clean when examined at the filter capacitor, of 2.3 V peak-to-peak, of which only a small amount was required by the audio stages. It is quite instructive to view these waveforms and to try to figure out what they mean.

### Automatic Gain Control Another interesting circuit in the receiver is the AGC, or automatic gain control, shown at the right (also called AVC, automatic volume control). This is feedback tending to keep the level of the signal at the 2nd IF amplifier constant, independently of the strength of the signal, and is done by rectifying the signal and using the resulting voltage to change the bias on the 1st IF amplifier, so that its gain changes. A larger IF signal should result in a lower base voltage, which reduces the collector current, and with it the gain. The AGC and the detector are combined in one circuit. The time constant of the AGC must be long enough that it does not follow modulation changes, while the audio filter must remove the 455 kHz IF, and not attenuate the modulation frequencies. The AGC time constant is roughly 10 μF times 3.3k, or 0.033 s, corresponding to 30 Hz. The time constant of the ripple filter is roughly 0.01 μF times 2.2k, or 22 μs, corresponding to 45 kHz. The audio fits nicely between 30 Hz and 45 kHz.

The AGC works by controlling the collector current of the 1st IF stage. The emitter resistance re is 25Ω divided by the collector current in mA, and the gain of the amplifier is inversely proportional to re, since it is a common-emitter amplifier with emitter resistor bypassed. The 0.02 μF capacitor has a reactance of about 16Ω at 500 kHz, so the emitter is well bypassed. With no AGC voltage at all, the collector current in the first IF stage would be about 6.0 mA. By actual measurement, the collector current in operation varies from about 0.55 mA with no station tuned to about 0.10 mA with a strong station tuned in. The resistance re varies from 45 to 250 ohms, changing the gain by a factor of 5.5. Notice how the rectified IF signal creates a negative voltage to reduce the bias for a strong signal.

There are integrated circuits that perform the functions of mixer or IF amplifier, and so forth, and even integrated circuits that contain the complete superheterodyne receiver. These are conveninent, but do not illustrate the principles as clearly as the discrete-transistor receiver.

### Frequency Modulation

A sinusoidal signal whose instantaneous angular velocity is ω = ωo + mωs cos ωs, where ωo is the carrier angular velocity and ωs is the modulation angular velocity, is said to be frequency modulated. The quantity m is the modulation index, equal to the maximum frequency deviation divided by the modulation frequency. The main advantage of frequency modulation is that it is free from the effects of atmospheric noise or "static" that affects only the amplitude of the wave, since all the information is in the frequency variations.

Using this angular velocity, we find the signal to be e = E sin(ωot + m sin ωst) = E Σ Jn(m) sin(ωo + nωs)t, where Jn is the Bessel function of order n. Just as in the case of amplitude modulation, there are sidebands, but here an infinite series of them. Fortunately, most of the energy is concentrated in the lower sidebands for smaller values of m. For m = 1, the J's are 0.77, 0.44, 0.11 and 0.02 for the first four sidebands. Most of the energy is located within 3ωs of the carrier frequency. For m = 5, however, the numbers are -0.18, -0.33, 0.05, 0.36, 0.39, 0.26, 0.13, 0.05 and 0.02, and the energy is spread over about 7 sidebands.

The FM broadcast band is assigned 88-108 MHz, in the middle of the TV broadcast bands, with a channel width of 200 kHz, allowing 100 channels. The maximum frequency deviation permitted is ±75 kHz, the maximum modulation frequency 15 kHz. At the maximum modulation frequency, then, m = 5 and the energy will be spread over about 105 kHz on either side of the carrier, just exceeding the channel width. By comparison, the AM broadcast band of 540-1600 kHz contains 106 channels of width 10 kHz. The IF of an FM receiver is typically 10.7 MHz. Some receivers may be dual-conversion, converting the 10.7 MHz IF further to 455 kHz, making it easier to offer an AM/FM receiver in one unit.

It is very easy to create an FM signal with a voltage-controlled oscillator (VCO), and to demodulate it with a phase-locked loop. However, broadcast FM receivers do not use PLL's, but other forms of detectors that will be looked at here. Phase-locked loops are treated on another page of this series. It should be mentioned that advanced modulation techniques make it possible to transmit two audio channels over the same FM channel, allowing "stereo" broadcasts.

The operation of FM detectors is widely regarded as mysterious, and this view is not far from wrong. Here we shall study the ratio detector to find out how it works, without going deeply into the theory at this point, or studying other forms of FM detector that are also used, and somewhat similar. It is necessary for an FM detector to give an output voltage that is proportional to the deviation from the center frequency, a much more difficult job than AM detection, and one that cannot be performed by a simple mixer. A circuit demonstrating ratio detection is shown at the left. It was simply rustled up from what I had available, and is not recommended as a practical demodulator. The transformer, in particular, seems ill-suited to the purpose, since the primary inductance was only about 0.8 μH, requiring a capacitor as large as 0.1 μF to resonate it at some frequency less than 1 MHz. If you can find a transformer with a higher primary inductance, your demodulator will probably work much better. Choose the capacitor so that the resonant frequency is around 500 kHz, which is convenient for us. The lead to the center tap of the secondary would have a blocking capacitor in it in a normal receiver circuit, since the primary would have a DC bias.

Feed the circuit with an FM signal from a function generator, using any sort of input to the FM jack. Look at the ouput with the oscilloscope at the point marked AM out, set for DC. Set the rest frequency of the function generator at the resonant frequency of the primary tuned circuit. The DC offset control of the function generator making the FM control voltage can be used to make small changes in the input frequency. Adjust this voltage so that the demodulated signal is as good as possible (mine was rather distorted, but I had made no effort to optimize the circuit at all). If you remove the modulation, and vary the amplitude of the signal, you will find that the ratio detector is not sensitive to the level, one of its advantages. Some FM demodulators respond to the amplitude as well as the frequency, so the signal has to be limited before detection. This is not necessary for a ratio detector.

The circuit works the following way. The signal that goes directly to the center tap of the secondary splits equally there, and is rectified by the diodes to create equal voltages across the two capacitors to ground, in a kind of voltage doubler action. The signal is also applied to the tuned circuit, and when it is exactly on the resonant frequency, the diodes are also equally affected, and the capacitor on the right is charged by the equivalent half-wave rectifying action. The voltage across this capacitor is equal to the sum of the voltages across the two capacitors to ground. When the frequency varies from resonance, a phase shift is produced that is either capacitive or inductive, depending on the direction of deviation, which increases the current through one diode while decreasing it in the other (by vector addition of the currents). The total voltage across the two capacitors to ground remains constant, constrained by the capacitor at the right, while one increases and the other decreases proportionally to the frequency deviation.

It is essential to have a tuned circuit, tuned to the center frequency of the FM signal, in an FM demodulator. The action of the demodulator depends on the changes as the frequency varies from the center frequency. Tuning is, therefore, more critical for the FM receiver than for the AM receiver.

### Function Generator Chips

There are integrated circuits that produce sine waves, although they are really relaxation oscillators and the sine waves come from shaping a triangle wave. Examples are the ICL8038, which is good up to about 100 kHz, and the newer XR-2206 and XR-3038, which can oscillate up to 1 MHz. The XR-2206 has some interesting features that illustrate some of the topics mentioned in this page, so let's examine this chip.

The XR-2206 provides a square wave at an open-collector output, as well as a sine wave. It can produce a triangle wave, but this is really just a step towards the sine wave, and is seldom required. The frequency is set by a capacitor, in the range 0.001 - 100 μF, and a timing resistor of no less than 1k, but preferably between 4k and 200k. There are actually two timing resistors, and which one is used is selected by the level on pin 9. When pin 9 is open or above 2 V, the resistor called R1 is used. When pin 9 is below 0.8 V, R2 is used. This gives easy frequency-shift keying (FSK) by a logic input to pin 9. A circuit for testing the XR-2206 is shown at the right. The 25k pot adjusts the symmetry, and the 500Ω pot adjusts the waveform (so the data sheet says). I found the 25k control to be best about in the center, and the pot adjusted to 203Ω. The 50k pot adjustment is also important. This circuit sets the average value of the output waveform (here to 6.0 V) and its amplitude. If the amplitude is not set correctly, the waveform will have flat tops or bottoms, or both. I found 38.6k the best setting. It is nice to have the pots to see what they do, but if you don't have them, use fixed resistors instead (2 - 12k, 200Ω and 39k) and you should be all right. The proper adjustment of these controls is necessary for a good-looking sine wave. The XR-2206 makes a quite passable sine wave.

The frequency is about 1/RC. I found 10k and 0.01 μF to give 9759 Hz, 100k and the same capacitor 1018 Hz. 1k and 0.001 μF gave 664 kHz. Pins 7 and 8 are held at 3 V, and more than 3 mA should not be drawn from them, so 1k is the minimum timing resistor. The chip is advertised to work down to 0.01 Hz! I used a 10 μF tantalum (+ to pin 5) and R = 1 M, and found a period of 8.2 s, timing 10 oscillations with a stopwatch. Reducing R to 2k gave an ideal 20 ms period, or 50 Hz. The output was centered on 6.0 V, and its peak-to-peak amplitude was 6.0 V as well.

The XR-2206 has an AM input at pin 1. I used modulation at 1.0 kHz, 4.0 V peak to peak, and DC bias 4.0 V, for 100% modulation. The DC bias at this input is necessary, and the signal amplitude must be properly adjusted. The 664 kHz signal could be picked up on an AM radio at the expected frequency, and the modulation heard. I simply put the end of the whip antenna of the small pocket radio near the output of the XR-2206, and got plenty of signal. One could make a small AM radio transmitter with this chip for use over short distances. The output frequency can be modulated by an external voltage using the circuit shown at the right. R is the normal timing resisor, while RC handles the modulating current. The formula for the frequency is shown in the figure. If the applied voltage V is 3.00 V, the frequency is as determined by R. An increase in V lowers the frequency, and an increase raises it. Using R = 2.0k and RC = 1k, I could vary the output frequency from about 10 kHz down to 2 kHz by swinging V from about 1 V to 4 V. In any case, do not exceed 3 mA from pin 7 or 8. I was fairly close to the limit here, but RC = 2.0k for VC from 0 to 6 V would be OK. Use a buffered potentiometer to test the dependence of frequency on VC. Supply VC from a function generator, setting the DC bias at 3.0 V, and varying the amplitude over a small range, at a frequency of, say, 2 Hz, and watch the result on the scope. The waveform looks like a spring extending and contracting! Modulating the frequency with an external signal has quite a few applications. One is displaying frequency response on the scope--you might try this with a parallel resonant circuit. Feed Y and the XR-2206 with a triangle wave, and X by the rectified voltage across the tuned circuit. FM would also be good for testing a phase-locked loop.

The XR-2206 offers many possibilities for sine wave generation and modulation over a wide range of frequency. The output can be buffered to adjust its DC component and signal amplitude. Frequency can be varied by a range switch and a potentiometer, so that one could make a fairly useful function generator based on this chip, at low cost. With the XR-2211 FSK detector, it is easy to make an FSK data link.