Basics of amplitude demodulation

[vishnu36]

For effective demodulation of signal from amplitude modulated wave, is there a ratio to be maintained between carrier and signal frequency?. For eg: if carrier is say 10KHz, what can be the maximum signal frequency that will ensure perfect demodulation at the other end? can it be 1KHz?

 

[FvM]

Presume you are asking about DSB with carrier and simple envelope demodulation method. In this case, a sufficient condition is that carrier can be filtered by a low-pass. 1 kHz should work well, also higher modulation frequencies if necessary.

 

[dick_freebird]

A lot depends on what kind of signal quality you're looking for,
out the back. A 10X carrier is going to be OK for "digital" (see
demodulator ICs which advertised lock in <= 10 cycles) but it
will nohow be adequate for a 0.1% THD+mumblemumble.
I think there probably is, but do not personally know, some
relation between AC signal fidelity and "Nyquist*2^Nbits"
for a desired bit-count-fidelity on an analog signal. Or SNR,
driven by the per-carrier-cycle "error residue" from too
coarse a "sampling".

 

[D.A.(Tony)Stewart]

There is a complex relationship with the quality of the demodulation method with linearity and carrier synchronization. Passive demodulation is possible with adequate filtering. Synchronous demodulation with ultra-linear multipliers and coherent carrier PLL generation gives superior results in both AM and FM systems between the carrier to noise ratio (CNR) and signal-to-noise ratio (SNR). FM has the deviation ratio k improvement when k>1 and frequency ratio of carrier/signal (fc/fs >>1). The complexities are difficult for me to express mathematically here.

More popular is to combine signals in quadrature modulation to improve the carrier bandwidth efficiency, just as analog TV does with phase modulation of two signals on a sub-carrier without interference between luminance AM carrier and audio sub-carriers.

Here is a demo of a 1 kHz carrier with a sawtooth stepped every carrier cycle and ramped with 16 carrier cycles and another slow sawtooth stepped every 16 cycles of the other sawtooth.
The 1st plot combines both inputs.
The 2nd plot shows the carriers in slow motion 5ms/div
The 3rd plots shows the separated carriers below and the synchronous AM demodulated outputs above.

The modulator block with ABCDE has a dual linear multiplier and adds both quadrature carriers.
pour s'amuser

 

[WA9VEZ]

The old theory, before Shannon showed us a better way, was 1 bit per second required 1 hertz. Under the newer theory, if you think about signal to noise power, then by using multiple levels of encoding larger than the noise power, you can exceed the 1 hertz per bit concept. Thus you can trade off bandwidth versus signal to noise signaling power with proper encoding and use greater transmitting power. In order to reach the theoretical improved data rates to bandwidth, avoidance of differential phase and gain errors in the transmission is achieved by predistortion prior to transmission, which will smear the data phase and amplitude constellations. Thus the maximum data rate for a channel is set by the expected ambient noise power, how much you have in your power budget to send the information, and an acceptable bit to error ratio. An example is MELPE vocoder transmissions using 200 Hz bandwidth that have measured as providing greater intelligibility at the far end than an unencoded transmission.

 

[FvM]

I think there probably is, but do not personally know, some relation between AC signal fidelity and "Nyquist*2^Nbits" for a desired bit-count-fidelity on an analog signal. Or SNR, driven by the per-carrier-cycle "error residue" from too coarse a "sampling".

Good question. An ideal AM modulator (e.g. a multiplier as DSB modulator) obviously causes no signal distortion as long it keeps the integrity of the baseband signal, in other words satisfies the Nyquist criterion. The same applies to a synchronous demodulator which also does a simple frequency shift and mirroring but doesn't create intermodudation products or harmonics. But how about an envelope detector as demodulator? I modeled it as ideal full wave rectifier and it looks like that it also doesn't distort the baseband signal. My conclusion is that there are no additional restrictions to an AM demodulator than Nyquist.

 

[D.A.(Tony)Stewart]

10:1 Frequency ratio is marginally ok under ideal conditions but this limits the usefulness in most applications. In order to amplify weak signals the wide bandwidth of AM-DSB with 10:1 results is 20% of the carrier frequency in signal bandwidth which makes it very difficult to block out adjacent channel noise with brick wall filters with the desired SNR depth. The PLL multiplier methods also relies on perfect frequency and phase matching to avoid errors in demodulation of the amplitude. This gets easier as the modulation bandwidth moved towards smaller % bandwidth meaning higher carrier:signal ratios.

You can read a bit more here about the linear multiplier or "product method"

Wikiwand - Product detector

A product detector is a type of demodulator used for AM and SSB signals. Rather than converting the envelope of the signal into the decoded waveform like an envelope detector, the product detector takes the product of the modulated signal and a local oscillator, hence the name. A product...

www.wikiwand.com

 

[FvM]

I don't hear a reference to radio transmission or noisy signals in the original question, as I understand it's asking about the basic properties of AM modulation and demodulation and its restrictions. Noisy channels and foreign signal blocking are respectively beyond scope. AM demodulation as such is restricted by Nyquist, the necessity of limiting the modulation index below unity to use envelope detection and the problem of separating baseband and carrier by filters.

 

[KerimF]

For effective demodulation of signal from amplitude modulated wave, is there a ratio to be maintained between carrier and signal frequency?. For eg: if carrier is say 10KHz, what can be the maximum signal frequency that will ensure perfect demodulation at the other end? can it be 1KHz?

It seems you didn't read yet:
Prj01 - A Simple Reliable Double Sideband Suppressed Carrier (DSB-SC) Demodulator | Forum for Electronics (edaboard.com)

This simple demodulator (having also a lock range) works for any AM index, from m=0 (no modulating signal) to m=infinity (no carrier).

Kerim

 

[FvM]

I also don't see a reference to suppressed carrier in the original question, but I agree, it's unclear in this point.

 

[KerimF]

@vishnu36​

For instance, after discovering this simple reliable modulator in year 1979 (though it is not known yet even in these days) I used DSB-SC in the 80's for many years to scramble my private RF links by which I fooled all conventional receivers. So, while there was a conversation on the air, the radio listeners heard it as sort of noisy interference (on MW band) or blank channel (on FM band)... You will find all necessary technical details on its thread.

--- Updated Apr 20, 2023 ---

I also don't see a reference to suppressed carrier in the original question, but I agree, it's unclear in this point.

The lock range of my demodulator, with or without a carrier, can also be adjusted at will though there is a practical limit which could be known for a well defined project.

Anyway, I fully understand that humans in general are made to believe AI sources even more than themselves sometimes.

--- Updated Apr 20, 2023 ---

For example, in a real link (for FM band), I modulated a voice signal of 5 KHz bandwidth a suppressed carrier whose frequency was 32768 Hz (instead of 38 KHz),

 

[D.A.(Tony)Stewart]

> For eg: if carrier is say 10KHz, what can be the maximum signal frequency that will ensure perfect demodulation at the other end? can it be 1KHz?
For perfect demodulation, you may need perfect noise free environment to get perfect demodulation .
In the practical world, engineers define expectations on acceptable perfection or "specs" which includes the carrier, signal range and noise signal range and bandwidth with specs on signal/noise ratio SNR

Hypothetical example DB AM fo 1kHz signal used 2kHz BW

Consider a 10 kHz BPF with 2.5 kHz BW @ -3dB and at -40 dB @ bandstop = 5kHz with 1.7 dB equal ripple in the 12th order BPF passband
Op Amp needs 1GHz GBW due to the extremely high Q poles to define the steep skirts.


However, if you shift the carrier up to 100 MHz FM Band then using the AM carrier as an FM sub-carrier so traditional narrowband filtering is possible and easier. Then Kerim's fine example of DSB-SC AM sub on FM carrier using a ratio of fc=32768 Hz, Fs 0 to 5000 Hz for a minimum ratio of 6.4 is doable with synchronous demodulation.

Otherwise you might need a filter that looks like this.

 

[KerimF]

Then Kerim's fine example of DSB-SC AM sub on FM carrier using a ratio of fc=32768 Hz, Fs 0 to 5000 Hz for a minimum ratio of 6.4 is doable with synchronous demodulation.

I wish I have time and a real interest now to find out the lowest practical limit of this ratio, in this special case, which has to be <6.4 but surely >2.