A better, faster way to test open-loop gain

In systems that use feedback, the feedback network is a circuit that is configured to achieve a specific gain and phase relationship, such as an adjustable proportional integral differential (PID) controller that adjusts the gain or phase of the loop to ensure stability (see Figure 1). We often need to measure the performance of this feedback network in a specific configuration in order to model its open-loop characteristics. However, such tests are always difficult. For example, the low-frequency gain of an integrator can be very high, which is generally beyond the measurement range of common testers. Therefore, the purpose of these tests is to quickly characterize the network frequency response with a minimum of effort using existing tools and a small amount of specialized circuits.

Figure 1 A basic feedback system

Q: You make a lot of sense. I have a real project that I would like to get your advice on.

Answer: Please speak.

Q: To qualify a recent project, I have been using a programmable feedback network and have been asked to collect real data to verify that it is meeting the required performance. To collect the data, I sized up the test equipment I already had and connected it together to form a crude open-loop test system using a IEEE-488 interface board, a simple digital oscilloscope, and an arbitrary function generator (see Figure 2).

Figure 2 Functional model of the test system

I used an existing GPIB interface development software library and wrote a program to collect the data points for drawing the Bode plot, which is very similar to the manual drawing of Bode plots we learned in engineering college. The function generator is set to output a sine wave, and the frequency of the sine wave is gradually changed as the "input" of the system. Then, the input and output of the system are measured with an oscilloscope, and the gain at a given frequency point is calculated from this.

A: So what was the result?

Q: After running the DUT through multiple iterations, the problem of exceeding the scheduled time for open-loop measurements using standard lab equipment became apparent. High-precision measurements require many data points, and for each data point, a significant amount of time is spent simply exchanging data between the software and the test equipment. The resolution of the oscilloscope also plays a role: triggering becomes difficult when input amplitudes are small because noise dominates the system. I also observed intermittent erroneous samples (see Figure 3). Analyzing the erroneous samples, I found that they occurred before the test equipment had finished updating, which was actually a system stabilization time issue. In the end, each test took an incredible 35 minutes. When analyzing how this time was used in the test, I found that for each data point, most of the time was spent communicating between the host and the test equipment, rather than actually testing.

Figure 3 Data samples collected from three different tests of the same structure

A: Execution time can be improved if hardware functions are used instead of software routines. For example, using the existing I2C serial bus on a programmable device ^will take less time to transmit ASCII characters to form a text-based command message. With this adjustment, several abstraction layers and command interpretation operations are eliminated from the test loop, resulting in precise and direct control of system operation.

Q: So, what hardware circuits will be needed to implement such a testing method?

A: Use a broadband direct digital synthesizer (DDS), such as the AD5932 ^1, to replace the function generator. This DDS can provide excellent frequency range and high-quality sine wave output for your design. When using the AD8307 ² logarithmic amplifier and a differential amplifier, gain measurement becomes very simple. The last key acquisition system hardware is an analog-to-digital converter to replace the digital oscilloscope. Using a multi-channel input ADC, such as the AD7992 ³ or AD7994 ^4, will reduce the total cost of the system. In this way, we can use two of the existing channels to acquire the results of the logarithmic amplifier and then use software to complete the difference calculation. The modified test structure is shown in Figure 4.

Figure 4 New test system block diagram

Q: How is gain measurement performed using a logarithmic amplifier?

A: With an ac input, the low-cost and convenient AD8307 logarithmic amplifier will produce a dc output into a 50-ohm load that is equivalent to 25mV/dB of input power (0.5V per decade). The AD8307 has a 92-dB dynamic range and can be used to measure very small input signals in high-gain open-loop circuits. While you are not actually driving a 50-ohm load, this scheme will allow you to calculate the gain (in dB) using the difference between the outputs of the two AD8307 devices that are testing the input and output of the signal.

Q: Can you explain this in more detail?

A: Let's briefly review how to calculate logarithms: