# Difference between analog signal and battery voltage

I want to find out if using an analogue sensor is feasible in my noisy environment by running some signal integrity tests before I buy it. Because I dont have the sensor yet, I need to simulate its output. This can be assumed to be a constant DC voltage, since it will change very slowly. A reasonable value for this voltage is 2.25VDC.

My approach to model my sensor is to take a 9V battery and load it with four 220K ohm resistors in series. I will use the potential difference between the last resistor and ground (2.25V) to model my sensors analog output, and run my tests with it.

To make this more clear, an example of a test I will run is to use one ADC module to measure the voltage across the last resistor in the potential divider, and another ADC module to measure the voltage across the wires of the other end of a slip ring connected across that last resistor while it is rotating. Some more background to understand the application if you're curious is at this question.

My question is can an analogue signal be modeled by a battery? What is the theoretical difference between an analogue signal and the voltage across a batterys terminals other than the source resistance?

Thanks for helping a beginner to signal processing!

• There are several models that each depend on what you are trying to accomplish. – Andy aka Feb 5 at 20:24
• Very approximate modelling to start to get a basic understanding of what noise to expect. If it succeeds the initial testing I'll have to look into more elaborate approaches. – user211492 Feb 5 at 21:05
• You have already accepted an answer, but I think you should consider the issues that @dim brings up regarding the ADC. – Elliot Alderson Feb 5 at 22:25
• The voltage across a battery is an analog signal, by any reasonable definition. – Hot Licks Feb 6 at 2:20
• I don't see why you need a battery at all, you could just connect wires to your adc with a resistor on one end to simulate the input impedance of your sensor. That will tell you how much noise to expect. Ways you could improve that noise is to add termination resistors near your ADC, add ferries, shielding around your cabling, using a differential ADC & twisting your wires etc. This mostly assumes you are worried about induced noise and not system noise. Also, this might be a good read ni.com/white-paper/3344/en/#toc4 – THEMuffinMan7 Feb 10 at 9:02

## 3 Answers

The simple answer is: yes, in many cases a simple voltage source & resistor (Thevenin) model is enough to model the output of a circuit (there are theorems to that effect). Formally, you would need a voltage source & a complex impedance, to also be able to represent the frequency behavior. But it can be even more complicated than that.

Some of the factors that this will not be modeling:

• Sensor noise. You would need to explicitly add a noise source to represent this.
• Sensor non-linearities. This is a linear model, circuits will behave differently if current or voltage limits are exceeded.
• Sensor instabilities. Many circuits become unstable under some load conditions (for example inductive or capacitive loads). Although this could probably be represented with more elaborate impedance models, the interaction with non-linearities makes it complicated.

But if you (1) ignore the sensor's noise contribution, (2) don't exceed loading limits, (3) don't exceed stability limits, and (4) frequency response is not a concern, then yes, you can model it with an adequate battery and resistor combination.

• For now my tests are very approximate so I am not too concerned about noise, non-linearity, and instability. But those things are good to know about for later trials. Thanks for the response. – user211492 Feb 5 at 21:00
• @user211492 if I understand your application correctly from:[electronics.stackexchange.com/questions/419715/… 200kΩ is quite excessive to model this sensor, when it seems to have <470Ω output impedance. The large impedance will make any injected noise worse than what you will actually have with the sensor. – Edgar Brown Feb 5 at 21:06
• The source resistance is missing from the datasheet cdn.usdigital.com/assets/datasheets/… unfortunately. I will get that parameter from the company then choose an appropriately sized resistor to model. – user211492 Feb 5 at 21:43
• @user211492 not completely. As per you other question, they recommend the characteristics of the load, this gives a hint on the order of the source resistance. That's where I got that 470Ω from. If you carry out a more detailed analysis and assume that the designers knew what they were doing (e.g., sensor resolution given the load), you can get a more precise upper bound. – Edgar Brown Feb 5 at 21:45
• I will look for that in the Sedra and Smith book, thanks. – user211492 Feb 5 at 21:47

The idea is fine, but 220k seems rather high. You should check the specs of the ADC module, there should be an indication of the maximum input impedance (typically around 50k for ADC integrated to most MCUs). Use resistors with values lower than this.

Hint: you could also use a potentiometer instead of the lower resistors (closer to ground), so you can easily adjust the value. Keep at least one upper resistor and make sure you choose values that guarantee that the ADC input voltage rating is never exceeded.

My question is can an analogue signal be modeled by a battery?

Yes, as a voltage source with series resistance and a noise source. Batteries can be very low noise because of their low source resistance. You can even buy (or used to be able to buy) source calibration batteries that are only used for voltage calibration. Most analog amplifiers have a very high source resistance and pull very little current, so in most cases the source resitance of the battery can be neglected.

The best part about using batteries, is they are easy to shield and not connected to ground. This means that you can build a source, and not worry about 60Hz or other sources of contamination from RF getting into the signal with proper shielding.

What is the theoretical difference between an analogue signal and the voltage across a batterys terminals other than the source resistance?

A batteries voltage can be temperature dependent (some batteries more so than others), but most sources are temperature dependent. Other than that, analog electronics don't care what they are attached to, if you put the same voltage and source resistance from a battery or a signal generator, the analog electronics won't be able to tell the difference if the voltage is the same and the source resistance is the same. However it is the stability of voltage sources that makes the difference.