(*Editor's note*: *Signal Chain Basics* is an ongoing and popular series; click **here** for a complete, linked list of __all__ installments.)

(*Editor's additional note*: if you are not familiar with the principles and analysis of PID control: you should be; It is the most important, studied, understandable, and applied closed-loop control algorithms ever devised. There are many very good tutorials available at all levels and lengths.)

Temperature control using an analog proportional-integral-derivative (PID) controller can be a very simple, effective means of ensuring that the desired set point in a thermoelectric cooler (TEC) can regulate the temperature of a laser. The proportional-integral term works in tandem to accurately servo the current through the TEC, in an attempt to maintain the temperature set point of the controller.

At the same time, the derivative term regulates the rate at which this is achieved, thereby optimizing the overall system response. If the overall system response, H(s), can be characterized, then one of the most convenient and effective ways to design the PID controller, G(s), for this application is through simulation using SPICE.

*Step 1: Determine the thermal impedance of the TEC/Temp Sensor for SPICE Model*

To effectively employ SPICE as a design tool for a PID loop, it is important to capture the temperature loop’s thermal response to obtain the actual thermal resistance, capacitance, and transfer function of the PCB:TEC:laser diode:temp sensor connection.

Keep in mind that since the actual thermal characteristics can vary as much as 50 percent, it is best to inject and measure a thermal-step input into the actual system (with all devices soldered down) to obtain the best thermal model for a SPICE simulation.

Once the thermal connection is characterized, use an “outer loop, inner loop” procedure to determine both the overall loop response and stability of the controlling amplifier in the G(s) function. In each case, the outer and inner loop will be broken using a very large inductor and the loop excited via a large capacitor and AC source.

*Step 2: Break the outer loop between G(s) and H(s)*

The outer loop is defined as the path around the G(s) and the H(s) functions. The objective of the simulation using **Figure 1** is to break the outer loop to obtain H(s), G(s), and the overall loop gain to verify thermal loop stability.

*Figure 1: Simulation circuit obtains loop gain and phase.*

*(Click here to see enlarged image.)*

In this case, **Figure 2 **shows that the phase dips below zero degrees where the loop gain goes to zero dB, indicating that the entire loop is unstable. Therefore, modifying G(s) should both impose PID control and add stability to the temperature loop.

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*Figure 2: Loop gain and phase plot for Figure 1.*

*(Click here to see enlarged image.)*

The modified G(s) block in **Figure 3 **includes the PID elements. The corner frequency for the differentiator is set by R7 and C3; R3 sets the proportional gain; and C2 and R6 set the integrator corner.

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*Figure 3: Simulation circuit with compensated G(s).*

*(Click here to see enlarged image.)*

*Step 3: Break the “Inner Loop” of G(s) to determine the local amplifier stability*

The final step in creating the complete PID element is to check the stability of the local amplifier (OPA2314) by breaking the inner loop to ensure its stability separate from the overall loop gain. In this case the amplifier requires a 50 pF capacitor (**Figure 4**) to keep the local loop stable.

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*Figure 4: Final circuit with compensated local G(s) loop.*

*(Click here to see enlarged image.)*

References

•Green, Timothy, “Operational Amplifier Stability, Part 2 of 15: Op Amp Networks, SPICE Analysis” En-Genius (formerly AnalogZone), 2006.

•Simon Lenvkin, Sam Ben-Yaakov. “__PSPICE-Compatible Equivalent Circuit of Thermoelectric Coolers__,” Power Electronics Specialists Conference, 2005. PESC '05. IEEE 36th

•Chavez, J.A., Salazar, J, Ortega, J.A., and Garcia, M.J., “__SPICE Model of Thermoelectric Elements Including Thermal Effects__,” Instrumentation and Measurement Technology Conference, 2000. IMTC 2000. Proceedings of the 17th IEEE

Please join us next month when we will discuss how a poorly designed 20W amplifier can destroy 100W speakers.

**About the author**

*Matthew William Hann*, SAR ADC Product Line Manager at TI, has more than a decade of analog product and applications expertise which includes ADC’s, temperature sensors, operational amplifiers, difference amplifiers, instrumentation amplifiers, programmable gain amplifiers, power amplifiers, and TI’s line of ECG AFE devices. Through his previous role as an applications engineer, Matt developed a focused expertise on the design of analog front ends for medical applications such as ECG, EEG, EMG, blood glucose monitoring, and pulse oximetry. Matt received his BSEE from the University of Arizona, Tucson. He can be reached at ti_matthann@list.ti.com.

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