# 41-610 Output Frequency Response

Note: The 41-610 is no longer in production. However the contents of this page are relevant to many Arbitrary waveform generators so the content has been retained for support and use on other products.

The output frequency response of the 41-610 indicates the output is flat to within 0.5dB of sinx/x response; what does this mean? This page explains the frequency response statement.

## ARB basics

An ARB generates a waveform by clocking through a waveform stored in a memory device. In the case of the 41-610 the clock rate can be 100MHz, and the stored waveform is updated every 10ns at the ARB output.

The ARB is therefore an example of waveform generation by a sampled data system, and digital theory shows that if the waveform being generated is a sine wave then as the frequency of sine wave is increased the amplitude of the signal generated will drop. If the frequency of the sine wave being generated was the same as the clock rate no sine wave signal would be present on the output since the sine wave would be being sampled at the same voltage level on every cycle.

Normally the maximum frequency that can be generated by an ARB is considered to be half the clock rate, but even at this rate the signal will have alias signals present.

In practice the maximum useful sine wave that can be generated by an ARB is considered to be less than one third of the clock rate. For signals which have harmonic content in them an ARB can only reproduce the signal with a reasonable degree of accuracy if the highest significant harmonic frequency in the signal is less than one third the ARB clock rate.

## Sinx/x response

At lower frequencies if a variable frequency signal is generated (for example a swept frequency) the output level of the ARB will be observed to drop as the frequency increases. This is because the output has a frequency response which follows a sinx/x frequency response. The response is fundamental to all sampled data systems of this type - overcoming this response requires the file stored in memory to be pre-distorted to increase the level of the signal as the frequency rises. The effect is not due to deficiencies in the ARB and its amplifiers, it is a fundamental aspect of sampled data systems.

The graph below shows how the sinx/x response effects the output level of a sine wave generated from a 100Ms/s ARB. The horizontal axis is the frequency in MHz and the vertical axis the response in dB relative to the low frequency amplitude.

Sinx/x response for a 100MHz sampling rate, dB vertical and frequency in MHz horizontally

In the case of the 41-610 the specification is simply stating that the frequency response of the amplifier is flat to within 0.5dB relative to 30MHz, and at the output the response of the amplifier adds to the sinx/x response.

It should be noted that the sinx/x response factor is not just a high frequency issue. If the sample rate for the ARB is set to be low (for example 10MHz) then the sinx/x response will start at a lower frequency. So using a low sample rate to reduce the amount of memory required for a waveform will increase the influence of the sinx/x response.

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