Power, current, voltage transfer principles

[fog37]

TL;DR Summary

Power, current, voltage transfer principles

Hello,

I have been reading about impedance matching as being the main requirement to ensure maximum "power" transfer from one part of a circuit to another: the two electric systems $A$ and $B$ need to have complex conjugate impedance so only 50% of the energy is reflected back at their connecting interface to system $A$. Power is, in general, given by the product of voltage times current: $VI$.

what kind of applications/examples, beside power line transmission, require maximum power transfer, hence impedance matching, to take place? Some antenna applications? Some audio system? Why audio system?

What about maximum voltage transfer or maximum current transfer? What kind of situations demand those types of transfer? The general charging of a device simply require that the power supply source can provide the suitable voltage (indicated on the device cover) and can output enough current to charge the device itself. No maximum voltage/current/power transfer happens in that case...

At the end of the day, electrical power, which is electrical energy per unit time, is delivered in all cases...

Thank you!

 

[anorlunda]

Summary:: Power, current, voltage transfer principles

what kind of applications/examples, beside power line transmission, require maximum power transfer

That is a common misconception. The optimum impedance for a power grid generating source is zero. It was Thomas Edison who first realized that. Before Edison, the Electrical Engineering profession all believed in the max power transfer theorem.

The reason is simple. The max power transfer theorem presumes fixed source voltage. In power systems, we are free to set the source voltage to any value we want. It is not fixed. That's a good thing too, if we were limited by the max power transfer theorem, then 50% of all electric energy generated would be wasted as losses at the source.

In other applications, notably RF transmission, impedance matching is important.

 

[fog37]

thank you anorlunda.

What does it mean "...in power systems, we are free to set the source voltage to any value we want..."?

Could you give me an example?

 

[anorlunda]

The source is a generator. The generator voltage is adjustable.

 

[anorlunda]

Suppose the whole grid was a source generator with voltage V, and the load with resistance R.

The power is $P=\frac{V^2}{R}$. There is no maximum P.

 

[Joshy]

I'm not sure if "only 50% of the energy is reflected back" because that sounds pretty bad (maybe half of the power is dissipated from the source?), but I work with high frequency electronics, which frequently uses impedance matching.

Most of the work I've done is trying to make the load look like the characteristic impedance (textbooks often use Z₀ for its notation). Characteristic impedance is more like a wave impedance.. think of taking a flashlight and pointing it to a glass window. If you wanted all of the power from the flashlight to go to a load (like a chip or antenna) beyond the window, then the reflection would be very bad. The matching network used for impedance matching attempts to make the glass window "look" like more air to mitigate the discontinuities in characteristic impedance. If you're familiar enough with circuits, then it's like trying to make the Thevenin or Norton equivalent of the source or load to match each other. New students might be tempted to use resistors to mach the loads, but those dissipate power; so: matching networks used for impedance matching often use reactive elements such as capacitors and inductors.

You're right that there is a lot more to matching that includes concentrating on voltages and currents, but it's a highly specialized field if we continue talking about high frequency electronics. I've only had a brief look into it, but I want to do my graduate studies on radio frequency integrated circuits (RFIC) and I won't pretend to understand it very well. After so much matching networks and trying to get everything to look like Z₀... I've stumbled into the depths of low noise amplifiers (LNA) and power amplifiers (PAs), which are very common in RF electronics. What's so strange about these components... they are purposely not matched to the characteristic impedance. Again: Wont pretend to understand these very well, but I bring it up due to the original post and letting you know that there is more.

 

[zoki85]

That is a common misconception. The optimum impedance for a power grid generating source is zero. It was Thomas Edison who first realized that. Before Edison, the Electrical Engineering profession all believed in the max power transfer theorem.

Didn't know Edison was that smart

 

[anorlunda]

I think the Edison story is interesting but obscure. The book Edision, His Life and Inventions is available free. Chapter X, Edison's Dynamo Work is about the controversy. It's too long to quote here, but here are a few teasers.

But perhaps the most serious drawback lay in the high-resistance armature, based upon the highest scientific dictum of the time that in order to obtain the maximum amount of work from a machine, the internal resistance of the armature must equal the resistance of the exterior circuit, although the application of this principle entailed the useless expenditure of at least 50 per cent. of the applied energy
...
Electricians and scientists of the period had been accustomed for many years past to look to the chemical battery as the source from which to obtain electrical energy; and in the practical application of such energy to telegraphy and kindred uses, much thought and ingenuity had been expended in studying combinations of connecting such cells so as to get the best results. In the text-books of the period it was stated as a settled principle that, in order to obtain the maximum work out of a set of batteries, the internal resistance must approximately equal the resistance of the exterior circuit. This principle and its application in practice were quite correct as regards chemical batteries, but not as regards dynamo machines.
...
In June, 1879, was published the account of the Edison dynamo-electric machine that survived in the art. This machine went into extensive commercial use, and was notable for its very massive and powerful field-magnets and armature of extremely low resistance as compared with the combined external resistance of the supply-mains and lamps.
...
In the Scientific American of October 18, 1879, there appeared an illustrated article by Mr. Upton on Edison's dynamo machine, in which Edison's views and claims were set forth. A subsequent issue contained a somewhat acrimonious letter of criticism by a well-known maker of dynamo machines. At the risk of being lengthy, we must quote nearly all this letter: "I can scarcely conceive it as possible that the article on the above subject '(Edison's Electric Generator)' in last week's Scientific American could have been written from statements derived from Mr. Edison himself, inasmuch as so many of the advantages claimed for the machine described and statements of the results obtained are so manifestly absurd as to indicate on the part of both writer and prompter a positive want of knowledge of the electric circuit and the principles governing the construction and operation of electric machines.
...
[The critic said] How anyone acquainted with the laws of the electric circuit can make such statements is what I cannot understand. The statement last quoted is mathematically absurd.

Of course, every EE student today knows about dynamos/generators and their high efficiencies (~ 98%). Few however are taught about Edison's defiance of the EE profession of his day, and the ensuing controversy.

Full disclosure. I am an admirer of Thomas Edison.

 

[Tom.G]

Yes, Maximum power transfer from a source to a load occurs when their impedances match. However maximum power transfer is not always what is desired.

You will probably want to do some sketches/schematics and have a calculator handy.

Lets try a word picture of the situation. We will do it in DC because that is a lot easier to both describe and to follow. The same concept holds for AC (and RF).

1. We will start with a Limited Power source, where matching is desirable:
   • In the case of a real-world audio amplifier or a radio transmitter, there is an upper limit, depending on their design, of the maximum power they can supply, and you usually want to use all of that power that you can! To accomplish the matching, either a transformer or an impedance matching network is used to change the impedances that the source and the load see.
     
   • Assume a perfect power source, such as a battery, that can supply 2 Volts at 2 Amps, or 4 Watts of power.
     
   • Now since there are not many 'perfect' power sources, add an internal impedance of 1 Ohm in series with the battery.
     
   • If you measure the output voltage after the internal resistor you will measure 2 Volts, and with a perfect voltmeter you will draw zero current.
     
   • If you short the output (after the internal resistor) you will measure 2 Amps and zero volts.
     
   • Both cases yield zero power because either the current or the voltage is zero.
     
   • Now you connect a 1 Ohm resistor as a load. The voltage across the resistor will be 1 Volt and the current will be 1 Amp; showing 1 Watt of power to the load resistor.
     
   • So far it's rather straight-forward.
     
   • Now instead of a 1 Ohm load, calculate the power supplied to a 3 Ohm load. I get 1/2 Amp and 1.5 Volts. With the load getting 3/4 Watts.
     
   • Try it with a 1/2 Ohm load and see what you get.
2. Now we move on to the Electrical Power Grid where a constant voltage is desired.
   • As shown in the Matched case above, the load Voltage changes quite a bit when the load changes. If the electrical grid impedance was matched to the load in your house, the voltage would drop every time your washing machine or electric stove came on. Your light bulbs would dim and maybe your computer would crash.
     
   • To solve that potential problem, the impedance of the electrical grid is made very small relative to the load impedance.
     
   • Try the above calculations of the Matched Load example with the internal battery resistance set to 0.01 Ohm. Calculate for the same three load conditions.
     
   • Notice that with the lower internal battery impedance the voltage at the load stays almost constant, at least until you try to exceed the maximum current.

The Electrical Grid is designed to handle the peak power needed under any normal situation and its impedance is as low as practical to make sure the voltage does not vary by more than about 5% for any load combination. This does cause loss of overall efficency in that there is almost always enough power available, even if it is not used.

As for charging devices, batteries do not like a very rapid, high current, charge, they tend to start fires or blow up. The charging circuit limits the battery charging current to a safe value to avoid such things.

So that's why your computer does not crash when the washing machine starts.

A bit long-winded but I hope it helps!

Cheers,
Tom

 

[anorlunda]

The Electrical Grid is designed to handle the peak power needed under any normal situation and its impedance is as low as practical to make sure the voltage does not vary by more than about 5% for any load combination.

I almost always agree with @Tom.G , but not in this case.

Control of voltage on the grid in the range min to max load, has little to do with impedance. Control of imaginary power flow, VARs is the primary mechanism. There are also active controls, automatic voltage regulators, tap changing transformers, and switched capacitors. It is not a passive circuit. Also flow of real power to loads is primarily a function of phase differences, not voltage drops.

This does cause loss of overall efficency in that there is almost always enough power available, even if it is not used.

That is a valid but odd definition of efficiency, $\frac{power_{received}}{power_{available}}$ rather than $\frac{power_{received}}{power_{generated}}$.

 

[Tom.G]

@anorlunda, I concur.
And admit to heavy simplifying, hope it didn't cause undue confusion.

Tom