# AC Signals - Radians and Degrees? Why do we use both?

1. Oct 26, 2015

### tomizzo

Why exactly do electrical engineers represent sinusoidal signals with the frequency in terms of radians/sec but phase shift in terms of degrees? Why don't we represent the phase shift in radians?

I'm curious where/why this convention originated.

2. Oct 26, 2015

### BvU

Most EE I know use Hertz, not radians/sec to represent frequencies ....

3. Oct 26, 2015

### phinds

I'm curious to know where you got this idea since I agree w/ BvU that EE's use HZ. In fact, in my 50 years as an EE I can't remember anyone using radians/sec for frequency and if anyone had, I would really have had to scratch my head to figure out what he was talking about.

EDIT: I should add that I'm talking about in conversation. In some calculations, radians/sec might be used but it would be odd to express a final result, in conversation, with those units.

Last edited: Oct 26, 2015
4. Oct 26, 2015

### sophiecentaur

Using Hz is fine for general chat about frequency but, once you get into Oscillations and Calculus, you will get into a real muddle with 2π turning up every time you integrate or differential. Angular frequency (ω) makes life so much easier.
V=V0cos(ωt -kx) is much easier to manipulate than
V=V0cos(2πft - kx)
If you don't like the Maths then fair enough but twenty million flies can't be wrong.

5. Oct 26, 2015

### BvU

Flies ?

6. Oct 26, 2015

### donpacino

its a scalar. You can do the math any way you'd like and it wont make much of a difference, just 2 extra presses of the keyboard.

At the end of the day, when people review your findings, most would prefer it in Hz.
If you present the data in rad/s and they can't understand it, they probably should be reviewing your findings anyways.

7. Oct 26, 2015

### Staff: Mentor

We use radians/second for angular frequency. For example, 60 hertz is 377 radians per second.

When doing simulations or solving integrals, if we want the result of an integral to be in units of radians, then the integrand (frequency difference) is best expressed in radians per second. Of course you can always integrate frequency differences in hertz. The result will be expressed in fractions of a cycle, which could then be converted to radians. Same math, just awkward experessions.

8. Oct 26, 2015

### sophiecentaur

"Eat poo - twenty million flies can't be wrong" (Ancient philosopher)

9. Oct 26, 2015

### sophiecentaur

Yep.

10. Oct 30, 2015

In my opinion, since w*t it is an angle[radians] w=rad/sec it is not a “frequency” but an “angular velocity”.

However ,I think, we are speaking about frequency ["f"] from the expression 2*pi*f and “f” will

stay here Hz [or cycle/sec].

The phase angle shifting is connected with connection shifting symbol representing an hour on a 12 hours clock.

Here for each 30 degrees one has to add an hour. It will be inconvenient to use here radians -in my opinion.

11. Oct 30, 2015

### LvW

The angular frequency is w=2*Pi*f - and there are some people using the unit Hertz for this expression. However, this is WRONG.
The frequency f is given in Hz and the angular frequency w must be given in rad/s.
And there any many good reasons for using w rather than f.
For example, what is the impedance of a capacitor? Right - it is 1/wC.

12. Oct 30, 2015

### sophiecentaur

That seems valid to me but why would you want to change an established term? If we all know what it means there is no confusion.

Yes, the frequency in Cycles pre Second (Hz) is more readily appreciated and very commonly used in practical measurements. However, in theoretical descriptions - like, for instance, this, the elegance and symmetry of the form of the equation and the pattern that is revealed, using ω, speaks for itself. People who frequently use ω have no problem with it; they actually find a huge advantage in it. So there is little point in rejecting it - just because it's a bit of posy Maths. One should be bilingual.

Interestingly, the only times that frequency is actually measured in cycles per second is when someone stands there with a stop watch and counts cycles. Any electronic frequency counter could just as easily give answers in terms of ω but we would need a new unit (say Hzn) to denote natural frequency.

13. Oct 30, 2015

I agree with it. However, what about p*n/60=f or n[rpm]=60*f[Hz]/p[pole pair number]?
One needs w in a lot of calculation, of course ,but-semantically-it is still not a frequency ,just a angle velocity and it is frequency linked by definition[w=2*pi*f]- in my humble opinion. What Hamlet would say: words, words..

14. Oct 30, 2015

### sophiecentaur

There is a parallel here. We use dB (log10), Half Lives (log2) and Time Constants (logn). Most of us are happy enough with that. It's horses for courses. Get multilingual folks.

15. Oct 31, 2015

### meBigGuy

What do the units matter? You can deal with distance per time in many different scales, and with many different names. Km/hr. ft/sec, MPH, mach-1, 5C, furlongs per fortnight. What does it matter. It is the same concept for frequency (or inverse time). You use the units that make your ideas/solution/problem easy to express. None are correct or incorrect. Express them as Mega-rotations per moon-cycle if you want.

16. Nov 1, 2015

### LvW

meBigGuy - I totally agree with you, however: The units do matter because one should not forget to mention the units. Very often I have experienced that people using the term "frequency" without mentioning if the mean Hz or rad/s. Or they are using the unit "Hz" and mean the angular frequency. Hence, one has to be very careful using the correct units.

17. Nov 1, 2015

### sophiecentaur

But 'people' are generally pretty sloppy about such things. You only have to listen to conversation with the word 'dB' in it. e.g. "Is that dB Volts or dB Power?"
As long as the word "frequency" actually refers to Cycles per Second, then you can't go wrong. It's already been sail, above, that people who would have a difficulty with ω are probably not likely to need to use it.
But Units are not always just incidental. EM theory, using cgs and SI looks very different and it's not just a matter of swapping miles for kilometres. Of course, when you get to the botom of things, the PHysics is the same.

18. Nov 1, 2015

### Staff: Mentor

Multiplication by a constant does not change the units. Hertz are to radians/second as volts are to millivolts as cycles are to radians, as radians are to degrees, as $h$ is to $\hbar$.

19. Nov 1, 2015

### LvW

Correct (in principle), however - is (2*Pi) a constant or an angle in rad?

20. Nov 1, 2015

### Staff: Mentor

Are you seriously questioning whether 2 is a constant or PI is a constant?