I made some measurements via rigol scope and digital multimeter Fluke 87V and Uni-t UT60A.
I build this simply BJT sine-wave generator + opamp.
The output voltage was equal to 4V peak and the frequency was 64Hz.
When R1 = R2 = 100KΩ
The RMS voltage must be equal to

\( V_{RMS} = \sqr{Vdc^2 + \frac{Vac^2}{2}} = \sqr{5^2 + \frac{4^2}{2}} = 5.74V\)

And I was very surprised becaues only the scope show the correct RMS value. The Fluke and Uni-t show the same result Vac = 2.9V

And when I change R1 to 200K we have this voltage across R2

The scope math show Vrms = 4.37V. But multimeter's still show 2.9V

So the conclusion is that moder digital multimeter "show RMS" value but ignores the DC component.

 

I am not sure if you meant that the wave is ascending or it abruptly begins at 0,0 as collapsed part of wave or what??? Although it has a 32.0 degrees or as you have it -0.558 rads.

I was simply looking for an interval over which the combined AC + DC function is greater than or equal to zero volts. Since this a cyclical function an infinite number of integration interval options exist.

Another option might be from θ=5.725 to 9.983 radians etc....

The actual interval is .558+3.7 or 4.258 radians.

#2 When the ac goes below zero volts the diode goes off for 3.7 rads or at 3.7 rads. Is this at 9-17=-8 a.c.v.?

Yes

#3 The last of the f(x) intervals can't grasp how did 5.02 come about? That is 33.3+14.42+5.02+14.42.

Simply 9x0.558=5.02

The positive sign arises from the lower integration limit being negative [-0.558]

 

The derivation of the average value of a half-wave rectified 12V rms sine wave offset by 9V DC requires some more complex maths that simply adding 12V rms to 9V DC and so forth. I didn't post the math part. I simply gave the result.

A more obvious question from your perspective, is to ask why with only the 9V DC battery connected to the AC range of the meter [with the leads in one orientation] you measured about 20V, and about 0.6V with the leads reversed.

Would the cutting of the diode cause the .6 volt?

 

Possibly - depends on the instrument itself and how the rectification is done inside. Do you have a schematic of the meter? Speculation is probably pointless without that information being available.

 

Here's the schmatic of the Radio Shack analog meter ...

 

Hello

It is a halve wave

 

Yes it is. Which is a useful confirmation of the consistency of your observations.

Thanks to JoeJester for providing the schematic.

I'm not sure I can explain why the meter reads the 0.6V on reversal of the leads as indicated in your table of AC range measurements. Did changing the zero adjust have any effect?

It's rather hard to decipher some of the component values on the schematic e.g. the value of R30.

 

R30 is 5.1 M

here's the original jpg file ...

http://www.tech-service.net/pictures/RS_meter.jpg

 

Thanks JoeJester - that's an improvement. I just noticed there are two resistors annotated as R30. The other one is connected to VR2 on the lower side. Looks like a 5.6kΩ but I'm not sure. I'll bet the circuit was checked any number of times before publishing.

 

I'll bet the circuit was checked any number of times before publishing.

There's checking and there's rubberstamping. My guess is the latter in the majority cause of the errors in published material.

I wonder if the OP carefully adjusted the zero prior to their measurements or did they just flip the switch from DC to AC?

 

Yes it is. Which is a useful confirmation of the consistency of your observations.

Thanks to JoeJester for providing the schematic.

I'm not sure I can explain why the meter reads the 0.6V on reversal of the leads as indicated in your table of AC range measurements. Did changing the zero adjust have any effect?

It's rather hard to decipher some of the component values on the schematic e.g. the value of R30.

No, adjustment was in it appropriate place,in which I did use it at times for that galvanometer effect,placing needle in the middle of the scales. I am attempting to believe that it has to do with the superimposed voltage across the DC volt battery in some way.The probes orientation is + on + and - on - regarding the meter and battery.Although the main concentration was about the output across the resistor,which I don't believe that would effect the output anyway.The integral that you give on the reverse leads case across the resistor explained the 3.75 rms that I registered.But as it is said that the measurement is a function of the measuring device.And this one is more complex then D'arsonval type meters.So many possibilities.

 

Yes - understanding the limitations of the measuring instrument is essential to any measurement process. As Jony130 demonstrated, even supposedly true rms meters may not provide the expected indication.

 

Concerning the diode effect - you mention a value of 0.06V in your last post but noted a value of 0.6V in your first post - which is correct?[/QUOTE]
I did the frist experiment again and I must say the precision of the measurement is definitely a function of the instrument,which is me as the instrument this time.T_N_T was correct,the value is 0.06 or less but -0.06 volts and not +0.6 volts.I don't know would that make a different when I begain measuring for superimpose voltage or not, But I do appreciate the great feedback I have been getting from the AAC crew,thanks.

 

Nothing is ideal in this world - this is an active circuit in which the meter indication is "assisted" by the JFET amplifier bridge arrangement. While the circuit is well proven it will have its' limitations.

Given the meter was correctly zeroed before the measurements were taken, the uncertainty in explaining the observation persists. Whether the "discrepancy" of 0.06 V is due to circuit non-linearity or other factors is probably beyond our understanding at the moment. The rectifier diode D2 should have very low reverse leakage current, which should therefore translate to at least an order of magnitude less in the reading than the indicated 0.06V with the diode operating in reverse biased condition.

Just to reiterate the readings you originally posted ....

Component | A | B | C | D | Results | Direction
VR1 + - 3.3rms Forward
VR1 - + 23.94rms Forward
Vs1 - + 0.6 rms Reversed
Vs1 + - 19.8 rms Forward
Vs2 - + 12.06 rms Forward
Vs2 + - 12.0 rms Forward

Presumably it's the one I have highlighted in red that would be 0.06V.

It's interesting that the readings highlighted in blue [for the AC source?] show a 0.06V difference. Probably coincidence - or perhaps a small DC offset due to the DC current flowing through the AC source itself. Was the AC source a transformer?

PS: You were doing pretty well to "eyeball" readings to 10mV resolution on an analog scale.

I'm not sure I can contribute any further to the discussion.

 

Thevenin's Planet,

I'm assuming this is the face of your meter. I'll also assume you know about parallax and how to correct for that.

 

Nothing is ideal in this world - this is an active circuit in which the meter indication is "assisted" by the JFET amplifier bridge arrangement. While the circuit is well proven it will have its' limitations.

Given the meter was correctly zeroed before the measurements were taken, the uncertainty in explaining the observation persists. Whether the "discrepancy" of 0.06 V is due to circuit non-linearity or other factors is probably beyond our understanding at the moment. The rectifier diode D2 should have very low reverse leakage current, which should therefore translate to at least an order of magnitude less in the reading than the indicated 0.06V with the diode operating in reverse biased condition.

Just to reiterate the readings you originally posted ....

Component | A | B | C | D | Results | Direction
VR1 + - 3.3rms Forward
VR1 - + 23.94rms Forward
Vs1 - + 0.6 rms Reversed
Vs1 + - 19.8 rms Forward
Vs2 - + 12.06 rms Forward
Vs2 + - 12.0 rms Forward

Presumably it's the one I have highlighted in red that would be 0.06V.

It's interesting that the readings highlighted in blue [for the AC source?] show a 0.06V difference. Probably coincidence - or perhaps a small DC offset due to the DC current flowing through the AC source itself. Was the AC source a transformer?

PS: You were doing pretty well to "eyeball" readings to 10mV resolution on an analog scale.

I'm not sure I can contribute any further to the discussion.

I did not anticipate a further responds on the subject ,but "yes" it is a transformer with input @ 120 acv,60 hz. reducted to 12 a.c.v.I am in the process of getting orientated to measuring components and what to expect in regard to using the analog measuring devices.I guess it's kinda primitive but I come to understand from this method more detail about measuring devices gives me better insight on measuring the primitive sine wave and circuit behavior.A prerequested type of study excise.The sine wave is one of the Neanderthal I would assume.

 

The sine wave is one of the Neanderthal I would assume.

Quite the contrary - the sine wave is rather beautiful & full of simple wonder. A fascination and building block for pure & applied mathematicians. It's in the same class as the circle, I think. It's a wonder the poets haven't taken it up as a theme. "Ode to a sine wave"