T
Tim Wescott
Guest
On Fri, 01 Feb 2013 16:27:56 -0800, Daniel Pitts wrote:
Average voltage does _not_ equal RMS voltage, except for DC.
But I'm almost certain that any proof of that would end up requiring
calculus one way or another (for instance: appeals to AC power requires
use of the Fourier Transform, which requires use of calculus). So it
wouldn't be straightforward.
Of course, you could "prove" it pretty quick if you had a true RMS
voltmeter and some parts...
If you want to earn either his gratitude or his ire, point him to this
thread; he is certainly mistaken in his analysis.
--
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?
Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com
Sigh.On 1/30/13 8:42 AM, Daniel Pitts wrote:
On 1/29/13 9:40 AM, Mark Storkamp wrote:
In article <fgJNs.86314$LS5.49792@newsfe10.iad>,
Daniel Pitts <newsgroup.nospam@virtualinfinity.net> wrote:
On 1/28/13 8:25 PM, John Larkin wrote:
On Mon, 28 Jan 2013 18:34:05 -0800, Daniel Pitts
newsgroup.nospam@virtualinfinity.net> wrote:
On 1/28/13 4:37 PM, John Larkin wrote:
On Mon, 28 Jan 2013 13:23:11 -0800 (PST), George Herold
gherold@teachspin.com> wrote:
On Jan 28, 4:06 pm, Daniel Pitts
newsgroup.nos...@virtualinfinity.net> wrote:
On 1/28/13 12:03 PM, Tim Wescott wrote:
On Mon, 28 Jan 2013 10:48:59 -0800, Daniel Pitts wrote:
On 1/28/13 10:05 AM, Phil Hobbs wrote:
On 01/28/2013 12:45 PM, Daniel Pitts wrote:
On 1/28/13 9:14 AM, Phil Hobbs wrote:
On 01/28/2013 12:08 PM, Daniel Pitts wrote:
Hello Electronics Wizards,
So, I'm taking a Linear Circuits class at a local JC, but
due to
scheduling constraints I skipped the "AC" electronics
course. I
have
one
particular homework problem that I think I've gotten
correct, but
I'd like to have someone with more experience confirm.
Unfortunately
most of
my classmates finish the homework on the due-date, so I
can't compare notes.
The problem as stated:
Find the peak and average power delivered to Rl in the
figure:
.--o^-._-^-* -. 2:1 .---->|---o--.
| Fuse ^ | | Diode^ |
o S* || *S \
S || S /
120V rms S || S \ 220 ohm
S || S /
o | | \
| | | |
`-------------. .------.---o--.
|
-----
---
-
My approach to solving this is:
120v rms becomes 60v rms on the secondary of the
transformer. Assuming a
sine waveform, the peak voltage is 60v*sqrt(2), approx
85v.
Using the "ideal" model, the diode only conducts one
direction,
which cuts the Vrms in half.
Pavg = 30v^2/220ohm ~= 4watts
Ppeak = 85v^2/220ohm ~= 33watts
Does my approach look correct, or am I missing something?
If I am
missing something, a pointer to what I'm missing should be
enough. I
know I could get a slightly more accurate result if I
account for
the .7v drop, but I don't think the instructor cares, as
long as
I
understand that I could.
Thanks,
Daniel.
P.S. Sorry if this is a duplicate post, I think my NNTP
server
flaked out on the first attempt (as it does far too
often), but
I'm
not always sure.
RMS is a time average based on the power dissipated.An
ideal diode
in
the secondary side conducts on the positive half-cycle and
not on
the
negative half-cycle. On the positive, the instantaneous
current is
just the same as it would be if the diode weren't there,
and therefore the instantaneous power is also unchanged.
There's no
power
dissipated on the negative half cycle, so the average power
is half
of what it would be without the diode.
Power is proportional to voltage squared, so the RMS
voltage goes
down by a factor of.....?
I guess I don't fully understand what RMS is then... I
thought it
was
the square root of the average of the squares of all the
values - a
sort of Euclidean distance.
If I understand what you're saying, the Vrms would be
divided by 4
when the diode is in the circuit. This would lead to a Pavg
= 15v^2/220ohm ~= 1watt.
Is that the proper approach?
Thanks,
Daniel.
Power dissipated is RMS voltage squared divided by the
resistance.
That's the whole point of RMS--you can use AC or DC or some
nasty
switching waveform, but the RMS value will tell you how much
power
you'll deliver to the load, _on_average_.
Instantaneous power = (instantaneous voltage)^2/R
Average power = time average of instantaneous power
= 1/R * (time average of (instantaneous
voltage)^2)
(note the order of the operations--square first, then
average).
Then to get back to the right way to express the voltage,
equate the
two expressions for average power:
1/R * Vrms^2 = 1/R * (time average of (instantaneous
voltage)^2)
A little algebra gives
Vrms = sqrt(time average of (instantaneous voltage)^2)
i.e. you square, then time average, and then take the square
root,
which is where the name comes from: root( mean( square
voltage)).
Solving the equation for Vrms,
Vrms = sqrt(Pavg * R)
So if the average power is down by half, and R stays the
same, the
RMS
voltage goes down by what factor?
Cheers
Phil Hobbs
Ah, that would be a factor of sqrt(2). I think I've got it
now.
So, 60v rms input across a diode would result in 60v/sqrt(2),
or 42v.
That gives (60/sqrt(2))^2/220ohm = 1800/220 ~= 8 watts.
Is my analysis on Ppeak correct? 60v rms * sqrt(2) ~= 85v, and
85v^2/220ohm ~= 33watts?
Actually, is my analysis of what the transformer does correct?
It's probably close enough.
I would strongly suggest that you slap some graph paper down
and sketch
the voltage waveform seen by the resistor. Even if the
instructor doesn't need to see it, it should help your
understanding immensely.
I've seen, and sketched, enough half-waves that I'm not that
concerned
about seeing it. I do understand that much.
If you're on a track to be an EE and not just a technician, and
if you've
taken calculus, and if you have the time, you may want to take
your
sketch of the waveform at the resistor and calculate the RMS
voltage.
I'm on track to be a hobbyist, nothing more ;-). However, I
think you're correct that it my help me to do that work. Its
been a while since I've done any real calculus.
In this case, RMS would be defined as the square root of the
time average
of the square of the voltage. Finding the time average of the
square
of
the voltage can either be done intuitively (you know what the
time average is for a whole cycle, so you can easily do it for
a half cycle),
but grinding through the exercise of integrating the
voltage-squared
over
one cycle, then dividing by the cycle time, will be good for
your soul.
Yes, probably true. Deriving the formulas has always been a
useful exercise for me. I just didn't really have the time to
sit down with a
pencil and paper to do so. Maybe tonight.
Was my final answer of 8 watts for the Pavg correct?-
Grin, Here's another way to get to the answer. (Just to check
yourself.)
Without the diode what's the average power?
Then the diode blocks the signal for 1/2 the time so your answer
should be 1/2 the above number.... does that check?
That's a nice intuitive simplification.
You can imagine the transformer driving a resistor, no diodes, and
calculate the power, P = Erms^2/R.
Now split the resistor into two equal ones of resistance R, and
drive them from diodes in opposite directions. They conduct on
opposite half
cycles. The transformer still sees R, so the power delivered from
the transformer is the same, but by conservation of energy and by
symmetry
each resistor burns half of the power P. Now back-calculate the
RMS voltage across one of the resistors.
You can do similar intuitive thinking about complex signals by
splitting them up with ideal filters and dumping into equal
terminating resistors, then apply conservation of energy.
This is exactly the analysis I did originally, but according to
Phil Hobbs the analysis is wrong.
So, who is correct?
The diode doesn't (as you originally posted) cut VRMS in half, it
cuts the
power
dissipated by the resistor in half. I think that's the difference. I
think
you
corrected the VRMS thing in a later post.
Ah, okay. so I think I get it now. That makes sense.
Never bet against Phil on stuff like this.
Good to know ;-)
Incidentally, his book on electro-optics is worth having for anyone
serious
about electronics. The other necessary book is The Art Of
Electronics by
H+H.
Now that he's worked out the answer, it would be interesting to know
what his instructor expects the answer to be. I once took a community
ed night class at a local college. During the day the room was used
for a vocational electronics program. They had this same basic
problems worked out on the blackboard, but had the OP's original wrong
answer at the end.
Some of my classmates were comparing answers, and my answer was the
"odd man out". Others had calculated the average voltage. When I
explained how I got my answer (both the "intuitive" way and by
integration), they seemed very confused. One of them asked the
instruct about average power and average voltage. I'm not sure the
instructor was paying full attention but they said yes that would work.
Mathematically I can see it not working, so I'm sticking with my answer
and current understanding (Thanks Phil Hobbs), even if the instructor
does say it is wrong when he finally corrects the homework.
Anyway, thanks everyone for all your help. I appreciate it very much,
and I feel like I have a better grasp on this concept than many of my
classmates.
Ironic since most of them have taken an "AC" course, and I skipped
that one.
Yep, so the instructor has considered this approach and answer wrong...
His approach was to find the average voltage and use that in v^2/r. Of
course that isn't the answer I came up with... I used wolframalpha.com
to calculate my result:
http://www.wolframalpha.com/input/?i=r%3D220%2C+v%3D60+sqrt%282%29%2C+%
28integrate+%28v*sinx%29%5E2%2Fr+from+0+to+%28pi%29%29%2F%282pi%29
{r == 220, v == 60 Sqrt[2], Integrate[(v Sin[x])^2/r, {x, 0, Pi}]/(2
Pi)}
Unless I don't understand the definition of "Average" (sum over count,
or integral over range) or "Power" (current times voltage).
Average voltage does _not_ equal RMS voltage, except for DC.
But I'm almost certain that any proof of that would end up requiring
calculus one way or another (for instance: appeals to AC power requires
use of the Fourier Transform, which requires use of calculus). So it
wouldn't be straightforward.
Of course, you could "prove" it pretty quick if you had a true RMS
voltmeter and some parts...
If you want to earn either his gratitude or his ire, point him to this
thread; he is certainly mistaken in his analysis.
--
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?
Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com