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Extending the Usable Bandwidth of a Programmable Power Supply for Generating Sinusoid Waveforms

Tue, 12/10/2013 - 2:13pm
Paul Young, Agilent Technologies Inc.

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Figure 1: Diagram of programmable power supply with output terminals connected to the load capacitance (C) by load leads with total series inductance (L) and total series resistance (R).
 
  

Many applications involve generating sinusoid voltage waveforms onto low-AC-impedance capacitive loads. For example, this capability is needed when emulating automotive alternator whine for testing a car stereo system’s ability to reject noise. Such applications may require generating waveforms up to 20 kHz with peak-to-peak amplitudes of 500 mV onto a capacitive load as high as 1 mF to 1 F.

Because power sourcing combined with relatively high frequency for a DC source is needed, this type of testing generally involves a high-bandwidth power amplifier to source the AC portion of the waveform coupled with a power supply to provide the DC voltage. Very few programmable power supplies with the ability to modulate the output have the specified bandwidth to source high enough frequencies without attenuation, and audio power amplifiers won’t have sufficient sourcing capabilities to drive such low-impedance loads. Because of these combined capabilities, the types of power amplifiers used in this setup are often expensive and application specific. 

If a general-purpose programmable power supply for tests like these could be used, it could eliminate the need for such specialized, expensive amplifiers. It would also make the test setup much simpler, because the DC voltage and AC portion could be sourced from the same device.

Fortunately, a power supply's programming bandwidth limitation doesn’t prevent users from programming sinusoid waveforms above that frequency. Attempting to program a sinusoid voltage waveform beyond the specified bandwidth of a programmable power supply results in attenuation of the AC portion of the waveform. Because the attenuation is predictable, it is possible for users to quantify it for frequencies well beyond the nominal bandwidth. By calculating how to compensate for this attenuation at each specified frequency, users can source waveforms of desired amplitude up to frequencies well beyond the specified programming bandwidth. Users can effectively extend the usable bandwidth of a less expensive, nominally slower power supply for generating sinusoid waveforms. 

Power supply bandwidth
The primary limitation to the programming bandwidth of a power supply is typically the control bandwidth. The control bandwidth is the frequency at which attenuation will start due to the limitations of the feedback system that controls the voltage. For example, if a user programs a relatively slow sinusoid waveform whose frequency is well below the control bandwidth of the supply, the feedback system will allow the voltage on the output to easily keep up with the moving reference input. However, if a user tries to program a fast sinusoid waveform beyond the control bandwidth, the compensation won’t be able to keep up, and the output will be an attenuated and delayed version of the reference input. This feedback compensation is limited by design to ensure robust stability of the supply, and it may or may not be possible for you to change this compensation. 

Attenuation due to load setup
Another source of attenuation to consider is the load and lead setup. If a user has long load leads with series resistance and inductance and a large capacitive load, a two-pole LC filter will be formed. Even if the power supply itself were an ideal voltage source with infinite bandwidth, the sinusoid voltage seen by the capacitive load would attenuate significantly after the corner frequency of this LC filter. Users can predict the frequency response of the attenuation due to load configuration by calculating resistor, capacitor and inductor values, and their respective impedances at the frequencies of interest. 

For example, if a user has load leads with a total inductance (L) of 1 µH with series resistance (R) of 10 mΩ and a load capacitance (C) of 20 mF, the gain from “power supply terminal voltage” to “load voltage” will start to roll off after ≈ 1.6 kHz and quickly approach an attenuation rate of 40 dB/decade (Figure 1). In this example, programmed sinusoid waveforms with a frequency of 1.6 kHz will be attenuated by a factor of two from the terminals to the load, 5-kHz waveforms will see an attenuation factor of 20, and 16-kHz waveforms will see an attenuation of 200. The attenuation factor due to the load and lead setup multiplies by the attenuation from the power supply’s control bandwidth to yield total attenuation.

Minimizing the inductance and capacitance will maximize the frequency at which the attenuation starts.  The inductance is approximately 20 nH per inch of load lead length, so making the leads shorter will lower inductance. Twisting the positive and negative leads together can cut the inductance roughly in half for a given length, and using special low-inductance cable can lower it even more. It may be difficult to lower capacitance if the device under test requires a certain value. Equivalent series resistance, ESR, of the capacitor can limit the attenuation, but this will also limit the ability of the capacitor to minimize transient drop in the load voltage and filter voltage noise from the power supply.

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Figure 2: Measuring the attenuation of a sinusoid waveform with frequency (Fo) and compensating the amplitude of the programmed waveform to end up with a waveform of desired amplitude at the load.
 
  

Compensating for the attenuation
If users want to program discrete sinusoid waveforms of certain amplitudes whose frequencies exceed the above-mentioned bandwidth limitations, they will need to calculate or measure how much attenuation occurs at each frequency. The basic idea is to initially program a waveform with the desired amplitude at a certain frequency, measure the AC amplitude of the output waveform on the load, and divide the programmed amplitude by the output amplitude to get an attenuation factor. For programming waveforms at this frequency, you compensate the programmed waveform with the attenuation factor (Figure 2). Generating a table of attenuation factor versus frequency for a given load configuration will allow you to automatically compensate for the attenuation in all successive testing for the same load configuration.

Some more advanced modern programmable power supplies have digitizer capabilities and a measurement bandwidth well beyond the control bandwidth. These supplies can allow this process of measuring attenuation versus frequency to be done autonomously without the need for an oscilloscope to measure the amplitude. For instance, users could write a routine in MATLAB or Microsoft Excel VBA to program a sinusoid waveform of a given frequency, measure and calculate the actual amplitude of the output using the power supply’s digitized measurements of output voltage, and then calculate the resulting attenuation. A user could repeat this process for a set list of frequencies up to the maximum allowed by the measurement bandwidth. This would be especially useful if the load configuration setup was subject to frequent change and you needed a fast way to recalculate the frequency response. A prime example of a family of power supplies with this capability is the Agilent N7900 Series Advanced Power System.

Practical limitations to amplitude compensation
A user’s ability to compensate for the amplitude attenuation of a power supply does have several limitations. Consider a scenario where a user wants to program a 5-Vpp 20-kHz waveform with a 12-V DC level using a power supply rated at 24 V. At first glance, this seems to be within the ratings of the supply because the maximum load voltage will be 14.5 V and the minimum will be 9.5 V. The programming bandwidth is 2 kHz, so the attenuation due to the power supply might be around 14 if the compensation of the control loop is rolling off at 20 dB/decade. If the load leads have an inductance of 1 µH and resistance of 10 mΩ, and the load capacitance is 1 mF, the attenuation factor due to load and lead setup will be about 5. The total attenuation will be 70. Theoretically, you would have to program the sinusoid portion of the waveform to be 350 Vpp to end up with the desired amplitude at the output. Obviously, the power supply would not have the functionality to allow programmed values this large.  Users need to check that the compensated voltage programming waveform does not exceed the ratings of the supply, or the power supply will be unable to generate the desired waveform.

In addition, the internal protective current limitations in the power supply may inhibit its ability to source high-frequency waveforms with relatively large amplitudes. Even if the amplitude is within the ratings of the supply, the required slew rate may be too high for the power supply to generate the waveform. If a user attempts to program such waveforms, they may become distorted and somewhat triangular. This effect becomes worse for lower-impedance loads and higher-level DC current sourcing. If low distortion is desirable for the testing, it is good to check the actual output waveform to make sure it is a clean sinusoid. 

Conclusion
Extending the usable bandwidth of a programmable power supply can help users get more out of their equipment than they initially anticipated. It also allows users to purchase less-expensive equipment to perform the same tests.  

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