Agilent Technologies E1441A user service Creating Arbitrary Waveforms

Arbitrary Waveforms

Creating Arbitrary Waveforms

There are five built-in arbitrary waveforms stored in non-volatile memory. You can also download up to four user-defined arbitrary waveforms into non-volatile memory. Each waveform can contain between 8 and 16,000 data points. Topics covered on arbitrary waveforms are:

•Creating Arbitrary Waveforms

•Creating and Storing an Arbitrary Waveform

•Built-In Arbitrary Waveforms

For most applications, it is not necessary to create a waveform of any specific length since the function generator will automatically sample the available data to produce an output signal. In fact, it is generally best to create arbitrary waveforms which use all available data (16,000 points long and the full range from 0 to 4,095 DAC codes). For the Agilent E1441A, you do not have to change the length of the waveform to change its output frequency. All you have to do is create a waveform of any length and then adjust the function generator's output frequency. Remember, if you create an arbitrary waveform that includes three cycles of the same waveshape , the output frequency will actually be three times the value you set with the frequency command.

When creating arbitrary waveforms, you have control of both the amplitude quantization and phase truncation errors. For example, phase truncation harmonics will be generated when a waveform is created using the full amplitude range of the DAC (12 bits) but is created using only 1,000 waveform data points. In this case, the amplitude quantization errors will be near the noise floor while the time quantization error will produce harmonics near the -60 dBc level. Similarly, amplitude quantization harmonics will be generated when you create a waveform using less than the full amplitude resolution of the function generator. For example, if you use only one-fifth of the available amplitude resolution, amplitude quantization will produce harmonics below the -60 dBc level.

When importing data from instruments such as oscilloscopes, the data will generally range between 1,024 and 4,096 time points and between 64 and 256 amplitude points.

When creating arbitrary waveforms, the function generator will always attempt to replicate the finite-length time record to produce a periodic version of the data in waveform memory. As shown on the next page, it is possible that the shape and phase of a signal may be such that a transient is introduced at the end point. When the waveshape is repeated for all time, this end-point transient will introduce leakage error in the frequency domain because many spectral terms are required to describe the discontinuity.

Leakage error is caused when the waveform record does not include an integer number of cycles of the fundamental frequency. Power from the fundamental frequency, and its harmonics, is transferred to spectral components of the rectangular sampling function. Instead of the expected narrow spectral lines, leakage can cause significant spreading around the desired spectral peaks. You can reduce leakage errors by adjusting the window length to include an integer number of cycles or by including more cycles within the window to reduce the residual end-point transient size. Some signals are composed of discrete, non-harmonically related

46 Agilent E1441A Application Information Chapter 2