Controlling gain and modulation depth of long-tail pair as AM modulator?

Question

I'm investigating use of a differential pair as an AM modulator. The schematic below illustrates the general plan, but the values aren't really specific (not least because this isn't working yet!)

Here's the thing, as I understand it, the differential mode (normal mode) gain for this kind of circuit (with RE1 and RE2 as 0 ohms) is essentially Rc x Ic / 0.005. This I understand is derived from Rc / (2 x r'e), where r'e is the intrinsic resistance in the emitter, which in turn is (at room temperature) approximately 0.025 / Ic.

Now, my problem is this. I would like to achieve two things. First, a good "headroom" for the output swing, which would need me to set the values of the mid-point current through the pair and the value or Rc to get Q2's collector at about the middle of the 18 Volt supply. That's easy enough in principle, however, for my application I also need to keep the gain relatively low. Notice that the RF signal is about 300 mV p-p. I can't, therefore, have a voltage gain higher than 60 (and more likely less than half that to allow for modulation!)

But that's where my plan seems to fall apart, since to achieve the mid-point I need to get a drop of 9 V on Rc, which means that 9 = Rc x Ic, but at that point, the gain is fixed at 9 / 0.05 or 180.

Of course, the easiest way to reduce the gain of the differential pair would be to add an external emitter resistor (shown as RE1 and RE2, currently shown with zero ohm value), but if I do that I believe that I substantially reduce the amplitude modulation effect, since that depends on the variation of the total emitter resistance with the change of Ic, and making the total emitter resistance into RE(fixed) + r'e would mean that I'd lose (some of) the modulation effect. I'm not yet sure that I know how much I lose, and it might still be workable. I'm also not sure whether the modulation would become severely non-linear (I haven't worked out the math for any of this aspect).

So, I guess I have two questions, first am I missing something here, is there another route to controlling the gain and keeping headroom that I've not thought of? (I really don't want to have to divide down my RF input just to bump it back up again!) Second, is it likely to produce a workable, tolerably linear modulation, circuit if I add RE1 / RE2 as modest values, and if so, can anyone give me a pointer as to how to calculate the needed (audio) input swing to achieve 100% modulation?

^{simulate this circuit – Schematic created using CircuitLab}

Answer 1

Many modulators drive Q1:Q2 differential pair as switches, so linearity of the radio-frequency waveform isn't a big issue. However, harmonics of the drive waveform will have to be rejected. This can be done with a tuned circuit load at the modulator's output.

R2 helps Q3 stay linear, turning an input audio voltage into a linearly-changing current source for the differential amplifier.

To aid headroom, use a tuned-circuit load on the collector of the output transistor. This puts the average voltage on the collector equal to Vcc. At 100% modulation, the collector current falls to zero on an audio peak.
At the other extreme, Q1 or Q2 transistor must take all the current from Q3, and not saturate so that its voltage swings lower than its base voltage. For OP's example circuit, base voltage of Q1, Q2 differential pair is +9V. Q3 average current is 1mA. These two values establish the maximum collector load at Q2 collector output: 9k...this would require a tuned-circuit load instead of Rc.

With a tuned-collector load, you can drive Q1,Q2 bases with enough voltage to fully switch the average 1ma collector current from Q3: between Q1 and Q2. With no audio, Q1 switches 0.5 ma on/off, as does Q2:

How much audio achieves 100% modulation? Back-of-the-envelope calculation: since emitter voltage is 2V (average), +/- 2V audio input (2v peak-to-peak) should get you close to 100% modulation.
There really is no need to bias Q1, Q2 base at +9v...it could be at +5V, and still leave Q3 with enough voltage headroom. This will allow a larger modulator output voltage swing before saturation. It will also allow a higher output impedance too.

Edit:
Have added a detail on a finer time-scale showing how the differential pair (Q1-Q2) is driven to current saturation in non-linear fashion. Yet the current source (Q3) that supplies emitter current to Q1,Q2 still controls modulation linearly.
You can see that Q2's collector current is square-ish, yet its collector voltage is sinusoidal, thanks to the tuned circuit...all the harmonics of the 1 MHz RF signal are suppressed.
You might view Q1, Q2 as switches, switching Q3's current alternately, at a 1 MHz rate in this example.

• When Q3's current bottoms-out at zero mA, there's nothing to switch, and the modulator's RF output is zero: modulation is 0%
• When Q3's current tops-out at 2 mA, there's lots of current, and modulation is at 100%

So the linearity of Q3's ability to turn audio input voltage to its collector current is the primary quality of this long-tailed pair modulator.
The linearity of Q1, Q2's ability to switch RF between them isn't so important. It is important that these two switches spend equal time sharing Q3's current. We usually want each of Q1 or Q2 to conduct half the time: switching back and forth at a 1MHz rate.