What is the point of signal amplification if noise is also amplified?

Question

Sorry for my ignorance but there's is immense effort in electrical engineering in the topic of amplification. I can understand the reason for circuits rejecting noise or filtering noise, but have difficulty to grasp the reason behind signal amplification such as a single ended input output amplifier.

If signal is amplified the noise is also amplified so SNR will remain the same. SNR might even be worse because of the amplifying active circuit will introduce extra noise.

Can you give me a reason to amplify let's say a 0-50mV noisy signal to 0-3.3V range by a single ended amplifier which is coupled to a 0-3.3V 12-bit ADC? Or another example that makes the linear amplification important`.

EDIT UPDATE:

After reading the answers especially Spehro Pefhany's answer and the comments sections, I tried to quantify the estimate SNRs for both cases. I ignored external interference or ADC inherent thermal noise, I also ignored amplifier noise. I only used the 1mV rms signal noise and the uncorrelated ADC quantization error for calculations.

Please see the following equations in the Python code and let me know if there's any mistake:

import numpy as np;

ADC_range = 3.3
ADC_resolution  = 12
ADC_quant_error = ADC_range / (2**ADC_resolution -1)

# Without amplification
V_input_sig_range = 0.05
V_input_sig_range_rms = 0.05 / np.sqrt(2)
V_noise_rms = 0.001
V_total_rms_noise = np.sqrt(V_noise_rms**2 + ADC_quant_error**2)
SNR = 20 * np.log10(V_input_sig_range_rms / V_total_rms_noise)

# With amplification
V_input_sig_range_amplified = 3.3
V_input_sig_range_amplified_rms = 3.3 / np.sqrt(2)
V_noise_rms_amplified = 0.066
V_total_rms_noise_amplified = np.sqrt(V_noise_rms_amplified**2 + ADC_quant_error**2)
SNR_amplified = 20 * np.log10(V_input_sig_range_amplified_rms / V_total_rms_noise_amplified)

print(SNR)
print(SNR_amplified)

The above results as:

SNR = 28.795 dB

SNR_amplified = 30.968 dB

The difference is 2.17 dB

Answer 1

In the case of the ADC you should consider the noise the ADC adds.

If it's an ideal 12-bit converter and you are using 0-50mV out of 0-3.3V full scale you effectively have a 6-bit converter (5.95 bits). The quantization noise (even for an ideal converter) is quite large. Reality will be worse than this.

Answer 2

Preamplification is an engineer's cavalry. You put your best forces in the most strategic place so that the infantry can do its job at their skill level.

Low-noise circuitry is expensive and tricky. The job is not done by just picking specific low-noise opamps: thermal noise is everywhere. If you throw your expertise and the expensive parts and the high power requirements of low-impedance circuitry into preamplification, the further processing has lots more leeway to admit more noise: those additional noise levels will then be dwarved by the amplified signal noise.

Without preamplification, the whole processing chain has to be ultra-low-noise rather than just the first stage. That's much more difficult and ultimately more expensive.

Answer 3

Yes, analog design is kind of a lose-lose. Everything you do to a signal actually makes it worse (even filtering).

The goal is to make it better in the specific ways that your acquisition circuit needs.

Your ADC for example has a hard job of accurately digitizing a signal and it’s easiest to do on signals with certain properties - full scale voltage on the order of volts, and noise content below the sampling frequency.

Opamps on the other hand don’t mind tiny signals and with careful design your front end can condition a signal for accurate acquisition while losing less than you gain in the end.

Answer 4

There is a very obvious case where application is very useful: when your signal is going to be transmitted, whether over wires or wirelessly, where noise will be added during the transmission, so after the amplification.

Since the level of noise will not depend on the level of the original signal, your SNR at the other end will be greatly improved over a non-amplified signal.

50mV signal -> no amplicification -> transmission adds 50mV noise -> arg.
50mv signal -> amplification to 5V -> transmission adds 50mV noise -> yea!

While this is very true for transmission over longer distances, or over media prone to a lot of noise (e.g. wireless), this can be true over relatively short distances as well.

Answer 5

Can you give me a reason to amplify let's say a 0 - 50 mV noisy signal to 0 - 3.3V range by a single ended amplifier which is coupled to a 0 - 3.3V 12-bit ADC?

Sure: resolution.

A 12-bit ADC will have 4096 steps which, in the case of your 3.3 V ADC, will have a step size or resolution of 800 μV per step and a digital output of 0 to 4095. Ignoring noise that's a resolution of 0.025%.

The 50 mV signal, if unamplified, would only have a maximum of 0.050 / 3.3 × 4096 = 62 counts so the digital range would be 0 to 61. Ignoring noise, that's a resolution of 1.5%.

Or another example that makes the linear amplification important.

Audio amplification! The headphone output of your phone won't drive a large loudspeaker. An amplifier boosts the signal to a suitable level and power to put enough electrical energy into the speaker to put enough mechanical energy into the air.

If signal is amplified the noise is also amplified so SNR will remain the same.

And that's fine. If you're listening on headphones or on a large PA system the noise will be the same distance "below" the signal level.

SNR might even be worse because of the amplifying active circuit will introduce extra noise.

Yes, in general the signal degrades but high quality electronics can do a lot to keep the introduced noise and distortion low.

Answer 6

The point of amplifying analog 50mV signal to 3.3V to read the value with 12-bit MCU ADC is to use the full scale of the 12-bit range of 0..4096.

If you keep the value at 50mV, you have only range of 0..62 for the digital codes.

If you can work with 62 codes for the whole 50mV signal then that's fine, but 4096 codes for the 50mV signal may be better.

Answer 7

How noisy is your 0-50 mV signal? You didn't say, so I'll use a contrived example with some approximations for a back-of-the envelope analysis.

Case 1 - Apply The Signal+Noise Directly to the ADC

Your 12-bit ADC has an LSB of about 800 uV. Your 0-50 mV signal is about 6 bits (62 quanta), the lower 6 bits of this ADC (50 mV/800 uV about 62).

Now if your noise is 10 mV, that will affect/corrupt, 12 quanta of the ADC's output or a bit less than 4 bits. The information you care about will only be contained in 2 bits.

Case 2 - Amplify the Signal+Noise, Then Input to the ADC

Now say you amplify the signal so that your 50 mV, plus noise, signal uses the full range of the ADC. You would have to amplify that signal, and its noise, by 66. In this case, the 2 MSB's of the ADC's output would contain the information, and the lower 10 bits would just represent amplified noise.

So in both case you only have 2 bits (or a little more) of information content in the output of the ADC. The only difference is in which bits that information is contained.

Answer 8

There are many reasons to amplify a signal even if the S/N ratio becomes worse afterwards. For example, if your signal is a square wave 0-50mV and you want to drive a TTL circuit you need to amplify it otherwise you won't be able to trigger the input of a TTL chip as it requires much higher threshold input voltage to change its state. If your signal is an audio signal 0-50mV and you want to drive a speaker, then without amplification you won't be able to move the speker's diaphrame enough to produce sufficiently audible signal. If your signal comes from an output of a high impedance source and you want to drive with it a low impedance device you need to use impedance matching amplifier (or another impedance conversion device) to be able to do that. And many other reasons.

Answer 9

The amplifiers are used not to improve you SNR but for signal conditioning so you can use this signal on a way you want to use it. At first place, almost never your "load" impedance match your source impedance, and when saying match this no meen is the same, but is suitable for. An example, an ADC input is usually around 10 k , but there are many sources wit similar and impedance, as a result you signal will be attenuated, an in some case this can be also non linear attenuation. Having on mind that the input resistance ma depend on multiple factors, it's virtually impossible to compensate for that. Another good reason is to match the amplitude/current. If you drive a load that requires high current, or in case wit the ADC have predefined range this must be matched as well. If you have 100 mV pp signal you will never get the full ADC resolution, unless your reference is not 100 mV but that's not the case. To get the maximum from the ADC you want your max signal to be close to your Vref as amplitude. The amplifiers not only didn't change SNR but since they have theirs own noise they reduce it, but still are required. p.s And your calculation is not correct at all. What if you have a 10 bit ADC, 1.2 V reference and 1 mV signal ?

Answer 10

You are completely right. If you have an ADC with 0-50 mV input range, there is no need to amplify your 0-50 mV signal. However, you will need amplification if the input of the receiving device needs a larger voltage. Examples are: ADC with 3.3 V input range, a loudspeaker (think of several Watt), or a radio transmitter antenna (think of watts to kilowatts).

Just another detail: impedance. Even if the ADC is 0-50 mV, you will need an amplifier if the input impedance of the ADC is too low. The voltage amplification may be just the factor of one. The 'amplifier' is then called 'buffer'.

Answer 11

If signal is amplified the noise is also amplified so SNR will remain the same

No, it will not. If a signal is passed through an amplifier with power gain P, then the noise is amplified P times while the signal power is amplified \$P^2\$ times. Overall, the SNR is improved P times. But as you said, the amplifier will also add noise of its own so the improvement will be less than P.

Answer 12

Other than noise considerations, a further good reason to not only pre-amplify but pre-condition signals is that it enables good system design. I am going to use the example of an analogue audio mixer here.

The job of such a mixer is to take many audio signals from different sources, and enable them to be manipulated in all kinds of ways and then combined into any number of outputs. On a system level this is pretty complex; standardising on signal levels in the system makes things much easier.

Sources include:

• microphones with all kinds of varying senstitivities and of different types (some need DC phantom power, some don't). Always balanced, levels between about -60 and -10dBu.
• various "line" sources (e.g. playback devices, outputs from musical equipment such as guitar amps or "outboard" effects) which also have quite varied signal levels, between roughly -10 and +10dBu, some balanced, some not.

Within the console, there is a plethora of ways to filter these disparate sources and combine them into various outputs. Within the console, pretty much everything runs on (unbalanced) amp circuits, and generally power rails of +/-17VDC or so. Given that we generally want at LEAST 20dB of headroom to avoid clipping, it is usual to define an "internal operating level" which is typically around 0dBu (more or less).

So in practice we end up with a general purpose preamp which does the following:

• allow line or mic signals to be connected.
• for mic signals, allow switchable phantom power for mics.
• give a range of variable gain to allow external signals to be bought up to the internal operating level.
• give some sort of visible metering to show when signal level is "OK" or "too close to clipping" (at least a green/red LED).
• fery often , other useful features such as a dedicated filter to remove bothersome low frequency compenents ("plosives"), or to reverse the phase of a signal (useful when many mics are used together).
• providing good immunity to RFI or EMC
• giving some frequency tailoring ("DC to light" is NOT desirable), typically a gentle rolloff at 20Hz and 40kHz or so.

It's pretty hard to see how such a system would be usable without these preamps. An internal circuit such as an equaliser would still work at (say) -30dBu but the practical business of mixing would be just unmanageable.

The qualities of low noise and distortion are still very important and highly valued in this environment - but the preamp has a lot of other functions other than that.

Even in a more modern system (say a PC based system where signals are captured through a soundcard and then manipulated digitally) - we STILL care a lot about that preamp. Your internal processing might all be 32 bit floating point - but if you didn't first condition the signal well for the ADC, you are not getting the best results, because you are introducing more conversion noise or artefacts than you need to.

In summary : preamps are there to interface, amplify and condition external signals so that the system can be designed to work under known, controlled conditions.