What is systematic offset?

Question

I am bit confused about what exactly systematic offset is. I understood that generally offset could be due to two reasons:

1. Random offset which could be due to mismatch in size of transistors or any other component. This will be like noise with mean zero.

2. Systematic?

It would be great if you can provide an example with a differential pair or any such circuit so I strengthen my understanding.

Answer 1

Here is an example circuit with a systematic offset:

^{simulate this circuit – Schematic created using CircuitLab}

The bias current of a bipolar op-amp such as the venerable LM741 is not randomly distributed around 0nA, but rather always flows into the inputs (when balanced and under non-pathological conditions) and is typically 80nA. Schematic from datasheet:

If 80mV typical (500mV maximum) offset at the output is unacceptable you can add a 500K resistor in the path of the non-inverting input and the circuit will no longer have a systematic offset. Since the bias currents don't match perfectly and the resistors have tolerances there will still likely be an offset, just not a systematic one.

Answer 2

I had to look this up so take what I say with a grain of salt.

Just from the phrase alone, "systematic" means built into the system (or setup), not random.

Looking around for clarification, it means that even if the components are perfectly matched with perfect tolerance the offset would still be there due to fundamental non-idealities.

I couldn't think of such a situation, so I looked up some more. Apparently one of the most common causes of systematic offset (and systematic errors in general) is improper use or damage of measuring instruments. Which makes sense since it's an error inherent to the way you set up your system irrespective of tolerances or matching.

Random vs Systematic Error

Answer 3

Here's an example.

Say you have a bunch of RF amplifiers connected in parallel so as to give you a higher output. Forget for the moment about how this combining is done.

All real-world amplifiers exhibit some variability between parts. They may have slightly different gains, or slightly different noise figures, or slightly different gains as a function of frequency. Their characteristics also may vary with temperature or power supply voltage.

Those first two factors might be considered random, as their affects on the overall system are not correlated. If the gain of one part is slightly above the average, it's probably compensated for by another part who's gain is slightly below the average (assuming the amplifiers gain have some sort of gaussian distribution about a mean).

The second two effects - temperature and power supply sensitivity, would be considered systematic as they affect all parts the same. For example, many RF amplifiers have a negative gain coefficient with respect to temperature. That is, as the temperature increases, the gain goes down. This being the case, if the temperature of the system increases, the overall gain decreases. This decrease in gain wrt temperature would be considered a systematic error.

Answer 4

Systematic offsets of R_on and V_t

P-channel FETs have slightly higher R_ds,On than n-channel for the same size, so in order to equalize them in totem pole CMOS logic to a standard value for that logic family, the p-channel must be made larger to match the n-channel. The output impedance can be measured or specified by V_ol/I and (V_DD - V_oh)/I.

But they also have slightly different V_GS(th) thresholds, so at room temperature the input threshold may be balanced closer to V_DD/2 by design, but over the full temperature range the characteristic spans a broader range of offset by some +/- %.

Answer 5

A systematic offset would be like the DAC in the feedback path of a successive-approximation ADC, or some sort of auto-trim.

A systemic offset OTOH is there by design, like biasing a microphone amplifier to 1/2 V_CC so that a single-ended power supply can be used.