# Is there such a thing as a 'Constant Power Source'?

Academic question: Is there such a thing as an electrical constant power source, which delivers energy at a fixed rate?

Specifically ... there are voltage sources and current sources, which maintain (an approximation to) a reliable fixed voltage/current respectively. A current source will deliver electric charge at a fixed rate, charging a capacitor's voltage linearly; a voltage source will deliver magnetic flux at a fixed rate, 'charging' an inductor's current linearly.

I'm trying to figure out if there is a supply that could deliver energy at a fixed rate - a power source - so its voltage changes to whatever is necessary to deliver a current such that $$\VI\$$ is a fixed amount.

(I've tried Googling this, but the search is swamped by power supply ads, domestic power advice etc).

Guessing at its properties...

• it would treat voltage and current symmetrically! So a fixed power source would charge up a $$\1\mu F\$$ at the same rate as a $$\1\mu H\$$ inductor.
• it would charge a capacitor's voltage at a rate of $$\ V \propto \sqrt{T}\$$, because the energy is increasing linearly in time and $$\E = ½ CV^2\$$.
• same with an inductor's current.
• any resistor placed across it would dissipate the same heat regardless of the resistance - by definition. Doubling the resistance would increase the voltage by a factor of $$\\sqrt{2}\$$ and decrease current by the same.
• its impedance is ... undefined! Open circuit voltage is infinite (like a current source); closed circuit current is ... also infinite (like a voltage source). Hmm.

For extra points: any other interesting properties? Are they actually a thing? What would they look like?

• Yes. They are used for some experiments at a fixed power level (with some limitations). Sep 2, 2023 at 13:52

Academic question: Is there such a thing as an electrical constant power source, which delivers energy at a fixed rate?

Just consider a boost converter operating at a fixed duty cycle from a fixed DC supply with discontinuous inductor current (DCM) : -

Each time the MOSFET turns on, current ramps up in the inductor and, after a certain length of time, the energy acquired by the inductor is a specific and known value.

When the MOSFET deactivates, that inductor energy is released into the load. If this is done at a constant rate, then a fixed energy value is transferred to the load so-many times per second. That's the same as delivering a fixed output power.

It's probably less easy to see but, a flyback converter does this with a slightly higher level of "perfection" compared to the boost converter above. The boost converter will always deliver a certain residual energy to the load even when the MOSFET is never activated. However, the flyback's output doesn't piggy-back on the input voltage hence, it is a "more ideal" form of power or energy delivery system: -

In the picture above, the flyback converter is also shown to be equivalent to the inverting buck-boost converter. They both deliver a constant power to the output and, that constant power is dependent on duty cycle and input voltage.

The voltage transfer function of an ideal DCM flyback converter with turns ratio 1:1 is this: -

$$\dfrac{V_{OUT}}{V_{IN}} = D\cdot\sqrt{\dfrac{R_L}{2\cdot L_P\cdot F_{SW}}}$$

And, if you rearrange it you find this: -

$$\dfrac{V_{OUT}^2}{R_L} = \dfrac{V_{IN}^2\cdot D^2}{2\cdot L\cdot F_{SW}} = \text{power out}$$

Hence, the power out is proportional to duty cycle squared and input voltage squared. Of course, if $$\R_L\$$ rises too high, the output voltage of a practical design reaches a value where the output capacitor breaks down but, within practical limits, the flyback converter operated at a fixed duty cycle and fixed input voltage, is a constant power output device.

It's pretty simple to do with circuitry. The below circuit provides constant power at the output provided OA1 does not saturate, which limits it to something like 15A.

In reality the VCCS would also have limited voltage output compliance, which would show up in an inductor circuit.

simulate this circuit – Schematic created using CircuitLab

Here is what it looks like charging a 1F capacitor with 1W:

P.S. I used an op-amp with a multiplier because CircuitLab does not have a divider function.

• Of course, this requires an analog multiplier, which is non-trivial. Not impossible or anything, just complicated. Jan 16, 2021 at 0:57
• @Hearth Well, you could just buy an AD633, a bit expensive but does the job. Since that's a 4-quadrant multiplier it also raises the interesting issue of which polarity of voltage comes out of the constant power output, since one is as good as the other power-wise. Either + or - will work. Jan 16, 2021 at 1:02

I had considered the problem some years ago when asked about controlling some flexible PCB-style heater elements. The element plating thickness varied enough to be a problem with impulse power regulation and so constant voltage or constant current power supplies were not suitable.

I never built a solution but figured that it could be done using, for example, a controllable voltage source with the feedback coming from the product of the output voltage and current rather than the usual voltage-only feedback. I had considered using an analogue multiplier for the task.

This solution would be designed to work over a range of voltages and currents and so could only maintain constant power over a certain load range.

• Ha! This question arose exactly because my son was building a bank of light bulbs to use as a power-sink for testing some DC-DC converters, and we were admiring how the current leapt up before they heated up. And then he said "I wonder if..." :-) Jan 16, 2021 at 1:00

I'm trying to figure out if there is a supply that could deliver energy at a fixed rate - a power source - so its voltage changes to whatever is necessary to deliver a current such that VI is a fixed amount.

Well - there may not be in the sense of anyone having already built it, but you can certainly make one. In practical terms, multiply the voltage V_I from the current monitor by the output voltage, and use the product to regulate the voltage. How would you do the multiplication with a reasonable precision? Either by putting an MCU into the control loop, or by using a discrete time technique.

The LTC1043 switched capacitor building block has an example of a 0.01% accurate multiplier. That multiplier is fairly slow, though - the Y input is filtered through a 21Hz low-pass. But there are ways of speeding that idea up. The Y input stage is a voltage-to-frequency converter, and the X stage the multiplier. If one, instead, makes the Y stage a voltage-to-duty-cycle converter, e.g. using the LTC6992-2 voltage-controlled pulse width modulator running at 1MHz. This can be used to run a fast analog switch acting as a chopper that will multiply the X with variable duty cycle, performing the multiplication. This circuit will has Y bandwidth of about 100kHz for 1MHz PWM clock, and the controller using the multiplier output must have its bandwidth reduced to a smaller value to remain stable. Non-resistive loads may require lead/lag compensation.

Nothing can put constant power into a short or into an open circuit.

But within the parameters of its capability a switched mode DC-DC converter can be used as an approximate constant-power source if supplied from a fixed voltage and provided with the input current as feedback (instead of output voltage)

EG. I can buy this LM2596-based module for about two dollars, one of the trimmers sets an input current limit (effectively a power limit if the input voltage is constant). the other two set output current and output voltage limits.

Abstract:

This circuit delivers constant power to a varying load. Using a load-monitoring IC (MAX4210), it senses the load current and load voltage independently, and multiplies the corresponding signals together with an internal analog multiplier. Applying the multiplier output to the inverting input of an error amplifier lets you apply a control voltage to set the constant-power level.

This design idea appeared in the December 15, 2006 issue of Electronic Design magazine.

[...]

You can already see the challenges with defining a universal constant power source which delivers constant power into any load, such a device does not exist in a universal sense because power is dissipated by the load and not the source and so this behavior is load dependent and not source dependent.

. For a specific set of conditions or loads one can define such a device. For example a thermal controller may be designed to provide (approximately) constant power to a resistive thermal element by implementing load sensing and a voltage dependent current source which models the behavior of the element. In other words the source is designed for the load and a constant power application.

It is easier to define a power supply which consumes a constant amount of energy , which can be implemented with a ballast or energy dump that can accept the energy difference when the load does not accept it.

Constant power supplies exist to the extent that they are needed. Nearly all grid connected supplies adjust their output voltage and current to supply a pre-arranged power level. However the range of voltage adjustment necessary is very narrow. Such supplies are said to be grid-following. Battery charge controllers also deliver a relatively constant power level at a voltage that rises somewhat as the battery charges.