# Quantifying signal loss - should we use power gain or voltage gain?

We're researching communication with electrical signals through the human body (also called body coupled communication). We want to quantify the signal loss between a transmitter and receiver attached to a human.

The transmitter is a sine-wave generator in a wide frequency range from 50 kHz to 25 MHz, and the receiver is an oscilloscope.

The existing research sometimes use power gain, but most frequently voltage gain for this purpose. If I'm not wrong, the metrics are defined as:

$$Gain_{Voltage} = 20\, log\frac{V_{out}}{V_{in}}$$

$$Gain_{Power} = 10\,log\frac{P_{out}}{P_{in}} = 10\,log\frac{V_{out}\cdot I_{out}}{V_{in} \cdot I_{in}}$$

I'm confused as to which metric is more appropriate for our task.

Here are some problems in my understanding:

• If we use voltage gain, then we can maximize the voltage drop on the oscilloscope by simply using larger load resistance on the oscilloscope (e.g. configure it to use 1M ohm instead of 50 ohm.) It seems wrong to do so, as the oscilloscope and its parameters are not really part of the communication channel we want to measure.

• On the other hand, power gain is maximized when the input and output impendances are matched (which makes more sense.) Since the ultimate goal is to have a working data transmission over the human body, I'm not sure if maximizing the current is important for this goal. It seems to me that when we use a simple modulation method like amplitude modulation, the signal-to-noise ratio on the receiver is directly dependent on the voltage alone. Does power gain matter for our application?

In "true" RF and telephony, it really is the power of the signal that matters, and thus power gain matters. That's because you can assume good transformers that'll preserve power while letting you customize the voltage gain and impedance match.

In a lot of applications, you're not looking for maximum power transfer or the best impedance match. In those cases you are, for instance, just sampling a voltage or a current and then amplifying it. In those cases, you care much more about voltage (or current) gain, and the power levels are of secondary or even no concern.

Which is a really wordy way of leading up to -- you may have to figure this out for yourself. Basically, if the signals in question are swamped by environmental noise no matter what impedance matching you do, then you just care about voltage ratios. OTOH, if impedance matching matters and it really is the amount of power going into your preamplifier that matters -- then you care about power ratios and thus power gain.

So does power gain matter for our application?

Yes it does.

Your receiver requires a signal that needs to be above a threshold power level in order for it to properly and reliably process that signal. You can apply voltage gain in your receiver circuit using many tried and tested ways but, if the power levels are too low, your received demodulated signal will be flaky.

It seems to me that when we use a simple modulation method like amplitude modulation, the signal-to-noise ratio on the receiver is directly dependent on the voltage alone.

That may appear to be true but, in reality, there will be circuit currents in your receive antenna that imply power is being received.

• That's not always true. Consider consumer AM radio, where the antenna is a tiny fraction of a wavelength. In that case you're either sampling the magnetic field with a coil and you just care about current amplification, or you're sampling the electric field with -- essentially -- a capacitve probe, and you just care about voltage amplification. In either case the atmospheric noise is far higher than thermal noise, so all that a perfect antenna match would get you would be more noise. Commented Mar 29, 2022 at 15:33
• @TimWescott I understand what you say but, in the case of AM radio using a ferrite rod, the antenna is immersed in the prevailing H and E field being received and, these are interdependent. Yes, the ferrite rod only uses the H field for producing a voltage but that prevailing H field is affected by the loading (and alter the localized E filed) and, there will be a maximum power point that is related to the bandwidth required. Commented Mar 29, 2022 at 16:11

In the RF/microwave world, people switch between power levels (dBm, for instance) and voltage (mV for instance) all the time, depending on what you're trying to analyze. This is fairly straightforward as usually your impedance is close to 50 ohms in all places along the signal chain.

But when it comes to gain, dB's are used almost exclusively. Things become simpler because gains and losses, when expressed in dBs, can just be summed. And since you are working with logs, the dynamic range of the numbers are reduced. Handling an analysis with a 130 dB or greater dynamic range is a lot easier using dBs than using voltages.

So like Tim said, it depends on your application. But I would think that in your application the impedance of the human body would fluctuate depending on where the path is and so voltage levels may be the appropriate measure to use.

• Thanks for the answer, but I think it's not what I was asking for. Both with power and voltage gains, we operate with dB mathematically (as in the formulas in my question). And for both, we need to measure mV or microvolt voltages in practice, to compute the gains. And the signal for loss for this application is actually less than 50 dB, it's not that great anyway.
– kfx
Commented Mar 30, 2022 at 9:32