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I am trying to understand AM modulation at circuit level.

As per theoretical framework, we have to multiply \$V_{G2}(t)\$, \$V_{G1}(t)\$, so that frequency shifting happens at carrier frequency, i.e., convolution in frequency domain.

Now as per the above circuit, using superposition, I can calculate the \$V_{out}\$ as \$V_{out} = R_1 \cdot V_{G2}(t) + R_2\cdot V_{G1}(t)\$, where \$R_1\$, \$R_2\$ are real valued and they are function of resistors, capacitors, and transconductance.

I am confused on how the circuit is multiplying the two voltages, it looks like the circuit is adding the two voltages, whereas it should multiply as per AM modulation. I am not clear on what's the purpose of \$C_3\$ and \$R_2\$.

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  • \$\begingroup\$ The circuit you have chosen is not a good example of a modulator in that it produces an AM signal almost as a bi-product due to non-linearities. Multiplying carrier with baseband produces a DSB signal - to get AM you need to add back the carrier - see slideshare.net/sghunio/chapter04-am-modulators \$\endgroup\$ – JIm Dearden Oct 10 '16 at 12:43
  • \$\begingroup\$ The nonlinear hFE is a function of emitter current , used here to multiply current gain of carrier signal to output. not a great modulator but it works \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Oct 10 '16 at 13:24
  • \$\begingroup\$ A better AM modulator can be realized using the classical transistorized differential amplifier (loing-tailed pair) if the BJT-current source in the common emitter path provides the carrier frequency. \$\endgroup\$ – LvW Oct 10 '16 at 13:36
  • \$\begingroup\$ hFE has pretty much nothing to do with modulation in that circuit. Vaudio just changes bias point linearly (in affine fashion really) \$I_\text{C,0}\approx(V_\text{B}-V_\text{BE}-V_\text{audio})/R_\text{E}\$. And then you have transcodcutance \$g_\text{m}\approx I_\text{C,0}/V_\text{T}\$ and finally carrier gain which is \$A_\text{v,carrier}\approx-g_\text{m}R_\text{C}\$. Not such a bad modulator all in all \$\endgroup\$ – carloc Oct 10 '16 at 17:03
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If \$V_{G2}(t)\$ is a carrier sine wave, then you can start the analysis by setting the audio voltage to zero. You'll find that the output is equal to \$G\cdot V_{G2}(t)\$, assuming operation in the linear region of the transistor.

In the calculation of the gain \$G\$, you'll find that it depends on the emitter current. Now let the audio voltage increase; this produces a reduction in the emitter current and a correponding reduction in the gain. If the audio voltage is negative, the emitter current increases, and the gain increases.

In other words, the audio voltage controls the amplitude of the carrier, and this is what defines amplitude modulation.

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The math you have used assumes the transistor circuit is operating in the linear region i.e. where current gain is largely fixed and (simplistically) does not vary with collector-emitter voltage. Theoretically, looking at it this way results in zero modulation.

So, step up the analysis and take into account non-linearities. These might be operating with the transistor in the saturation region i.e. the transistor starts to behave like a current controlled variable resistor. Alternatively look into the "early" effect because this can also be used to create amplitude modulation.

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