# PMMC and MI instruments

1. Feb 15, 2016

### cnh1995

How does a PMMC instrument read average value of a dc waveform? Is it true for pure dc or pulsating dc as well? I mean what will the meter show if I fed a full wave rectifier's output to it? Will it show its average vaue 2Vm/π? If yes, I don't understand how. Say the meter is an ammeter. So, the current will be pulsating and hence the torque will also be pulsating. How will the pointer come to rest at the average value on the dial? Is there any specific arrangement inside the meter or am I missing some key physics principle here? Same goes for a moving iron instrument. I know that the torque is proportional to the square of current but the current is alternating;hence the torque should also be pulsating. How does the pointer come to rest at the rms value on the dial?

2. Feb 15, 2016

### jim hardy

simple mechanical inertia. Think flywheel.
That's why most DMM's have an averaging filter before the ADC.

There's also some magnetic damping by eddy current in the brass or aluminum coil former. It makes a single shorted turn.
Some fine pocket compasses use that same principle rather than liquid fill.

3. Feb 15, 2016

### cnh1995

But how exactly on the average value on the dial? Why can't it be anywhere else? I mean for full wave rectificatied output, how does the mechanical inertia make the pointer stop at 2Im/π? What is the math involved here which relates this inertia to average value?

4. Feb 15, 2016

### jim hardy

are you taking a physics class?

inertia only keeps it from instantaneous movement all over the scale.
Where it comes to rest is determined by Force balance, sum of torques = zero
current causes clockwise torque
that's opposed by a coiled hairspring giving counterclockwise torque proportional to angular displacement
when the two are equal the needle stops

try a search on d'arsonval movement
http://www.tpub.com/neets/book3/7b.htm

and on T(orque)=NIABsinθ

http://helios.augustana.edu/~dr/203/203-s02/img/F29_20.jpg

^there's your electromagnetic torque proportional to current, NIABsinθ
and red spiral in other picture is the opposing hairspring that makes mechanical torque kX , where k is spring constant and x is angular displscement
NIABsinθ = kX ,
If you add inertia it looks like an invitation to oscillation, doesn't it ? Displacing force plus restoring force with no mention of damping? Harmonic motion?

Needle increases both its moment of inertia and damping from air friction.
The metal band on which coil is wound is a shorted turn for magnetic damping. To visualize magnetic damping look at videos of dropping a magnet down a copper tube.

get yourself a cheap analog meter and play with it, they're $9.95 at Walmart or ~$2 in junkshops.

above all have fun

old jim

5. Feb 15, 2016

### cnh1995

Ok. Suppose I fed a square wave of frequency 1Hz and duty cycle 25% to a PMMC voltmeter. Now, for 0.25s, there will be a current through the coil of the voltmeter and for the next 0.75s , there won't be any current, hence no torque. What will the meter read in this case? I guess it will read 0 since torque is 0 for 0.75s.

6. Feb 15, 2016

### cnh1995

I am studying EE..

7. Feb 15, 2016

### jim hardy

Have you taken statics and dynamics yet ? ∑forces = 0 in statics, ∑forces = ma in dynamics
You've asked a Dynamics problem : sum of the forces = moment of inertia X angular acceleration

You'd see the meter swing upscale then back down toward zero once per second.
A good high sensitivity test meter with long needle would never reach equilibrium.
Because its coil only gets about fifty microamps the needle moves slowly. Just not enough current to make much torque.
A less sensitive panel meter whose coil gets 1000 microamps might very well follow your 1 hz signal. You'd notice it's way less damped.
As you increased frequency the meter would appear to come to rest at position corresponding to average value.

8. Feb 15, 2016

### jim hardy

be aware that test meters respond to average but they indicate RMS.
That's achieved by lying. At each point on the scale they paint the number for RMS volts that'd cause that deflection instead of the number for average volts actually measured. So they only report the truth when measuring a sine wave . Surely you've studied RMS versus average for sine wave? I think it's .707/.636 ...
If you want to prove to yourself they lie - measure DC on the AC scale.

Many DMM's do the same thing.. check specs for words "average responding" or "true RMS"

9. Feb 15, 2016

### cnh1995

Aha..That's what I too was thinking! Thanks a lot! It was very helpful..

10. Feb 15, 2016

### cnh1995

Yes, it's roughly 1.11. So, they actually measure average value and paint the numbers 1.11 times the average values?? And that is for pulsating dc right? Because for ac, average is 0.

11. Feb 15, 2016

### jim hardy

Yes. Measure AC on the DC scale and it reads zero. You should try it with a real meter.
Be sure you're on a DC volt scale high enough for the AC you're testing . Those little wires of the meter coil will burn up at less than an amp.