SRS Labs SR850 manual Dynamic Reserve, What is dynamic reserve really?

DYNAMIC RESERVE

We've mentioned dynamic reserve quite a bit in the preceding discussions. It's time to clarify dynamic reserve a bit.

What is dynamic reserve really?

Suppose the lock-in input consists of a full scale signal at fref plus noise at some other frequency. The traditional definition of dynamic reserve is the ratio of the largest tolerable noise signal to the full scale signal, expressed in dB. For example, if full scale is 1 µV, then a dynamic reserve of 60 dB means noise as large as 1 mV (60 dB greater than full scale) can be tolerated at the input without overload.

The problem with this definition is the word 'tolera- ble'. Clearly the noise at the dynamic reserve limit should not cause an overload anywhere in the instrument - not in the input signal amplifier, PSD, low pass filter or DC amplifier. This is accom- plished by adjusting the distribution of the gain. To achieve high reserve, the input signal gain is set very low so the noise is not likely to overload. This means that the signal at the PSD is also very small. The low pass filter then removes the large noise components from the PSD output which allows the remaining DC component to be ampli- fied (a lot) to reach 10 V full scale. There is no problem running the input amplifier at low gain. However, as we have discussed previously, analog lock-ins have a problem with high reserve because of the linearity of the PSD and the DC off- sets of the PSD and DC amplifier. In an analog lock-in, large noise signals almost always disturb the measurement in some way.

The most common problem is a DC output error caused by the noise signal. This can appear as an offset or as a gain error. Since both effects are dependent upon the noise amplitude and frequen- cy, they can not be offset to zero in all cases and will limit the measurement accuracy. Because the errors are DC in nature, increasing the time con- stant does not help. Most lock-ins define tolerable noise as noise levels which do not affect the output more than a few percent of full scale. This is more severe than simply not overloading.

Another effect of high dynamic reserve is to gener- ate noise and drift at the output. This comes about because the DC output amplifier is running at very

SR850 Basics

high gain and low frequency noise and offset drift at the PSD output or the DC amplifier input will be amplified and appear large at the output. The noise is more tolerable than the DC drift errors since increasing the time constant will attenuate the noise. The DC drift in an analog lock-in is usu- ally on the order of 1000ppm/°C when using 60 dB of dynamic reserve. This means that the zero point moves 1% of full scale over 10°C temperature change. This is generally considered the limit of tolerable.

Lastly, dynamic reserve depends on the noise fre- quency. Clearly noise at the reference frequency will make its way to the output without attenuation.

So the dynamic reserve at fref is 0dB. As the noise frequency moves away from the reference fre-

quency, the dynamic reserve increases. Why? Because the low pass filter after the PSD attenu- ates the noise components. Remember, the PSD

outputs are at a frequency of fnoise-fref. The rate at which the reserve increases depends upon the

low pass filter time constant and roll off. The reserve increases at the rate at which the filter rolls off. This is why 24 dB/oct filters are better than 6 or 12 dB/oct filters. When the noise fre- quency is far away, the reserve is limited by the gain distribution and overload level of each gain element. This reserve level is the dynamic reserve referred to in the specifications.

actual reserve
60 dB	60 dB specified reserve

40dB

20 dB

low pass filter bandwidth

0 dB

freffnoise

The above graph shows the actual reserve vs the frequency of the noise. In some instruments, the signal input attenuates frequencies far outside the

lock-in's operating range (f >>100 kHz). In noise

these cases, the reserve can be higher at these

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