## May 18, 2021, 12 Noon PDT – Free Webinar

There are advantages that digital power electronics provides when compared to traditional analog control. These include:

- Flexibility
- Configurability
- Re-tuning the loop for component variation such as Electrolytic capacitor freeze out at low temperatures
- Management of the non-linearity of the converter
- Self-measurement of the loop response in closed and open loop.
- The ability to tune the switching times precisely to minimize the power loss and maximize efficiency.

All of these are very useful for power converter control. However, there are some differences with a digital controlled converter compared with an analog controller. These differences can be problematic if you are not ready for them.

### Numeric precision

The digital controller is made up from an analog to digital converter (ADC), some digital filters which implement the controller and then a digital to analog converter typically in the form of the pulse width modulator (PWM) or a variable frequency/period oscillator (VFO/VPO). Each of these has a limited number of bits and so determines the precision and noise performance of the entire system.

### Number of Bits

The analogue to digital converter has a limited number of bits. Typically, analogue to digital converters have eight, ten, twelve, fourteen, sixteen, eighteen or twenty bits. The increasing number of bits means increasing cost. Determining how many bits are required for the ADC is the first step in designing the digital controller.

The limited number of bits means that the measured output voltage or current is quantized, and the dynamic range is limited. This means that the precision to which the output can be controlled is limited to the step size in the ADC. If the precision is not accurate enough then the feedback loop will not be able to measure the difference from the required output value. Effectively the precision of the output control will be limited to the least significant bit step of the ADC. Typically, there is a trade-off between dynamic range and precision in the ADC. It is useful to use some precision extension techniques on ten- and twelve-bit ADC inputs to get both a high dynamic range and accurate output control. Precision extension techniques can include only sampling the error signal created with an analogue summing amplifier or using two ADC channels together to provide the precision and the range.

### Digital filter implementation

The internal calculations for the filters involve multiplications and additions. These are the typical MAC (multiply and accumulate) instructions in a DSP. These MACs realize the digital filters that provide the integrators, phase lift networks, differentiators and low pass filters that are used in closing the control loops. Each multiplication by a filter coefficient effectively reduces the precision of the signal. This reduction is especially noticeable in digital integrators and digital filters with narrow bandwidth. This loss of precision can, if it is large, lead to the digital filter failing to operate on small inputs.

Managing the digital precision of the digital filter is done by ensuring that as many bits as possible are retain in all the calculations by using coefficients that are chosen to maximize the retained signal level without clipping in large transients. Another precision extension system is the retention of extra result bits in the internal filter accumulators. This has a remarkably useful effect on reducing digital power control system noise.

### Power converter non-linearity

It is a usual to go to digital control with a new power converter development rather than swap analogue control for digital leaving the converter the same. This choice to update the converter along with the control is because the power losses, converter volume and converter costs are all required to be reduced and digital control can aid this.

So digital controllers are often applied to a new converter perhaps with MOSFET synchronous rectifiers, dual rate switching control or a complex LCL grid connection filter with synthetic damping. These new high-performance converters are chosen for extremely high efficiency and so necessarily have very low power losses. The removal of losses leads to the converters often having more variable control transfers with operating point changes and variable damping as energy loss has been removed. Along with this variability, the lower damping especially at light or no load, leads to converters that have no damping available to help with stability margins.

Some converters have extremely variable control characteristic. Measuring the converter behavior at many operating points is often indicated along with linearizing the power converter control transfer.

### Timer precision

The pulse width modulator (PWM) or variable frequency/period oscillator (VFO/VPO) operates from timers with a set time resolution from the clock. That is time is quantized. Thus, the period or duty of the oscillation or modulator cannot vary continuously as is can for its analogue equivalent. This quantization leads to errors in the control of the power converter. Consider the case where the timer clock runs at 40MHz. If the variable period oscillator register has 256-bits, then the maximum frequency that the VPO can make is 10MHz and the minimum is 39.0625kHz. The example LLC resonant power converter needs a variable frequency of 500kHz to 210kHz to perform the control. This means the VPO count register has a usable range from 80 to 191. This is 111 counts which is 6.8 equivalent bits or almost seven bits. If the processor has a 16-bit word, then the VPO precision removes 9 bits of accuracy and quantizes the control loop. Effectively the 6.8-bit precision is a quantization of available switching instants. The quantization is a non-linearity introduced by the timer accuracy.

The solution to the limited number of bits is precision extension modulation. This is the solution for the limited timer precision that occurs on microprocessors and digital signal processors when the converter switching rate is high.

Register for the webinar and learn about how to manage and exploit the limited timer precision and the limited number of bits.

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