🔬 Instrument Simulator

How to use it

How the bench is laid out

The bench has three columns and the signal travels from right to left. On the right are the sources, the two generators, with their outputs on the left edge of the front panel. In the middle is the processing: the multiplier, the adder and the two filters, each one with its inputs on the right edge and its output on the left, so the signal passes through them in the same direction in which it crosses the bench. And on the left is the measurement: the two oscilloscopes and the analyzer, with their inputs in a strip along the right edge.

With that layout each connector faces the instrument it belongs to and the cables run along the two aisles between columns. The only one that makes a loop is the one that goes from one module to another, because it has to exit on the left and enter again on the right, just as on a real bench. The five buttons above set up the connections of each example by themselves, and afterwards you can disconnect and try something else.

Each knob and each switch can be operated in three ways: by dragging, with the mouse wheel, or with the pair of little arrows beside it. The arrows move the control one step at a time and, if you hold them down, keep advancing on their own. They let you adjust without relying on a steady hand, which is what you need when you want to nudge the frequency a little at a time while watching the trace.

The generators

The frequency comes from two controls working together: the big dial gives a number between 0.2 and 2, and the row of buttons multiplies it by 1, 10, 100 and so on up to a million. Setting 1 kHz means leaving the dial at 1 and pressing the ×1k multiplier. Analog generators have always been operated that way, which is why they have that huge dial with the scale printed around it.

Both are the same model. In the examples we use generator 1 as the modulating signal, which is the signal that carries the information, and generator 2 as the carrier, the fast signal that carries it.

The oscilloscopes

The screen is divided into 10 divisions across and 8 vertically. That grid is the only ruler there is: the instrument does not say how big anything is, the switch does. If the VOLTS/DIV is at 2 V and the wave takes up 3 divisions in height, the signal is 6 volts peak to peak. If the TIME/DIV is at 0.2 ms and one cycle fits in 5 divisions, the period is 1 ms and the frequency is its inverse, 1 kHz.

There are two oscilloscopes and each has two channels, so four signals can be watched at once. That is exactly what you need to put the double-sideband signal, the AM signal and the two single sidebands side by side. Channel 1 draws in green and channel 2 in yellow, with a small dot of the same color next to each label, so you do not get confused when the two traces cross.

The VOLTS/DIV switch does not follow the 1-2-5 sequence of bench instruments but 1-2-3-5-7. The intermediate steps are useful: a 15 volt peak-to-peak AM signal runs off the screen at 2 V/div and looks small at 5, while at 3 V/div it takes up exactly five divisions.

The trigger is what holds the image still: it waits for the signal to cross a voltage level and only then starts the sweep, so every sweep begins at the same point of the wave. In AUTO, if the level is outside the signal the instrument sweeps anyway and the image drifts; in NORM it does not sweep and the screen stays black. When two very different frequencies coexist it is best to trigger on the slower one, which is why in the examples the modulating signal goes to one channel and the trigger takes its source from there.

The multiplier and double sideband

The multiplier delivers the product of its two inputs divided by ten. That division is not arbitrary: real multiplier ICs include that constant so that two ten-volt signals do not give a hundred, which would not fit within the power supply.

With the modulating signal on X and the carrier on Y, the product of two cosines gives the usual identity: two cosines at new frequencies, the sum and the difference of the originals.

That is a double-sideband suppressed-carrier signal. On the oscilloscope it is recognized because the envelope touches zero between one lobe and the next, and at each of those crossings the phase of the carrier flips: the picture seems to bounce off the axis instead of resting on it. On the analyzer it is recognized because there are two lines and in the middle, where the carrier should be, there is nothing.

The adder and AM

An ordinary AM signal is a double-sideband signal to which the carrier is given back, and that is exactly what the adder does.

The modulation index is therefore the peak amplitude of the modulating signal divided by the 10 V constant of the multiplier. With the modulating signal at 10 Vpp its peak is 5 V and the index is 0.5, or 50 %. Raising it to the maximum of 20 Vpp the index reaches 1, the envelope touches zero and the modulation is 100 %.

On the analyzer the difference is obvious: a third line appears in the middle, the carrier, taller than the two side lines. And the bandwidth does not change: it is still twice the modulating frequency, because the sidebands are where they were.

The filters and single sideband

If the information is complete in each sideband, sending both is spending twice the bandwidth to say the same thing. Single sideband lets one through and throws the other away. The oldest method to achieve it is the one set up here: you make the double-sideband signal and put a filter on it that cuts right at the carrier frequency.

The high-pass keeps the upper one and gives the upper sideband; the low-pass keeps the lower one and gives the lower sideband. Both filters are Butterworth, the response that is flat in the passband and is the one studied first, and they have the cutoff frequency and the number of poles at hand.

Here is where the real problem of this method appears. The two sidebands are separated by twice the modulating frequency, and to discard one without touching the other the filter has to fall off enormously across that span. With the modulating signal at 1 kHz and the carrier at 20 kHz they are at 19 and 21 kHz, just a 10 % difference: there is no reasonable Butterworth filter that separates them. That is why the single-sideband examples use a much higher modulating frequency, 8 kHz on a 32 kHz carrier, where the sidebands sit at 24 and 40 kHz and a 16-pole filter already rejects the unwanted one by about 30 dB.

In real radio equipment this is solved with a crystal filter or a mechanical one, working at a high intermediate frequency, where the gap between one sideband and the other is a few hundred hertz out of several megahertz. No network of resistors and capacitors comes close to that; the selectivity of a crystal is needed. By raising the filter poles and watching the analyzer you can see exactly how much it improves and how much is still missing.

And there is something worth looking at on the oscilloscope: the single sideband of a single tone is an ordinary sine wave, of constant amplitude and a frequency equal to the carrier plus or minus the modulating frequency. All the information ended up in the frequency. That is why an SSB signal cannot be demodulated with an envelope detector and the carrier has to be restored in the receiver.

The spectrum analyzer

The oscilloscope draws the signal against time; the analyzer draws it against frequency. Each sinusoidal component appears as a line standing at its frequency, and its height gives its amplitude. It is the same signal seen from the other side.

The controls are those of any analyzer. The center frequency and the span per division choose which piece of the spectrum is viewed. The reference sets which level corresponds to the top edge of the screen, and from there downward it is 10 dB per division. The marker is a vertical cursor that reports the frequency and the level wherever you place it.

The control that teaches the most is the resolution bandwidth. An analyzer does not see infinitely thin lines: each component is drawn with the width of the filter it uses to measure. If that filter is wider than the spacing between two components, the two look like a single hump. Lowering it makes them appear separate. With the carrier at 20 kHz and the modulating signal at 1 kHz you have to lower it below one kilohertz to be able to count the three lines of the AM signal.

With the marker placed on the leftmost line and then on the rightmost one you read the occupied bandwidth. For double sideband and for AM it is the same, twice the modulating frequency; for single sideband it is half. That is the whole point of SSB.

The oscilloscope display modes

• CH 1 and CH 2 show a single channel.
• DUAL shows both, each with its own sensitivity and position.
• ADD draws the sum of the two channels, which is what the vertical amplifier does when it is set to add. It is not the same as the adder module: here the sum belongs to the display and cannot be taken out through any connector.
• X-Y turns off the timebase and uses channel 1 for the horizontal axis and channel 2 for the vertical. With two sine waves Lissajous figures appear; with an AM signal on one channel and its modulating signal on the other the modulation trapezoid appears, which is the classic way to measure the index without counting divisions.

Two details of the bench

Outputs accept several cables and inputs accept only one. That is needed because the carrier has to go to two places at once to build the AM signal. In a real lab it is solved with a BNC T-connector, and you have to keep in mind that when you split one output between two inputs the load changes and the amplitude can drop.

The two modules that do arithmetic, the multiplier and the adder, clip the output at ±12 V, which are the rails of their power supply, and light a pilot lamp when that happens. It is the same limit that any circuit with operational amplifiers powered at that voltage has.

The front panels are inspired by the analog bench instruments that were used for decades in technical schools. They do not reproduce any particular model: they are generic panels built with the layout of controls that almost all of them share.