Vrms and dBV Meaning?

[guitarmd]

Here is a plot for one of my pickups. As you can see, it measures 3.0dB @ 1.80kHz. Simple enough.

The data is as follows, with the resonant frequency in bold colors. That would be 1800Hz, 3.040 Vrms, and 9.638 dBV.

Hz      Vrms   dBV   deg
100.0 2.160 6.670
200.0 2.188 6.779
300.0 2.209 6.865
400.0 2.237 6.971
500.0 2.277 7.128
600.0 2.294 7.192
700.0 2.356 7.423
800.0 2.423 7.666
900.0 2.487 7.894
1000.0 2.558 8.137
1100.0 2.642 8.418
1200.0 2.709 8.635
1300.0 2.770 8.829
1400.0 2.853 9.087
1500.0 2.925 9.303
1600.0 2.985 9.478
1700.0 3.031 9.610
1800.0 3.040 9.638
1900.0 3.001 9.524
2000.0 2.954 9.388
2100.0 2.852 9.083
2200.0 2.708 8.633
2300.0 2.574 8.191
2400.0 2.384 7.526
2500.0 2.229 6.942
2600.0 2.072 6.307
2700.0 1.936 5.739
2800.0 1.805 5.128
2900.0 1.662 4.414
3000.0 1.531 3.699
3100.0 1.422 3.060
3200.0 1.321 2.421
3300.0 1.228 1.786
3400.0 1.139 1.129
3500.0 1.067 0.565
3600.0 0.997 -0.027
3700.0 0.933 -0.598
3800.0 0.883 -1.081
3900.0 0.824 -1.684
4000.0 0.785 -2.103
4100.0 0.742 -2.596
4200.0 0.690 -3.218
4300.0 0.659 -3.627
4400.0 0.622 -4.123
4500.0 0.589 -4.602
4600.0 0.560 -5.034
4700.0 0.532 -5.490
4800.0 0.507 -5.909
4900.0 0.484 -6.312
5000.0 0.461 -6.734
5100.0 0.440 -7.132
5200.0 0.421 -7.506
5300.0 0.406 -7.834
5400.0 0.388 -8.216
5500.0 0.372 -8.582
5600.0 0.362 -8.819
5700.0 0.343 -9.291
5800.0 0.329 -9.668
5900.0 0.318 -9.942
6000.0 0.308 -10.230
6100.0 0.294 -10.631
6200.0 0.284 -10.930
6300.0 0.277 -11.156
6400.0 0.267 -11.464
6500.0 0.267 -11.486
6600.0 0.246 -12.177
6700.0 0.242 -12.342
6800.0 0.230 -12.780
6900.0 0.224 -12.991
7000.0 0.229 -12.812
7100.0 0.212 -13.484
7200.0 0.204 -13.791
7300.0 0.202 -13.894
7400.0 0.196 -14.139
7500.0 0.189 -14.487
7600.0 0.186 -14.625
7700.0 0.177 -15.023
7800.0 0.177 -15.052
7900.0 0.171 -15.368
8000.0 0.167 -15.537
8100.0 0.161 -15.841
8200.0 0.158 -16.006
8300.0 0.155 -16.214
8400.0 0.150 -16.502
8500.0 0.146 -16.729
8600.0 0.145 -16.748
8700.0 0.142 -16.963
8800.0 0.135 -17.390
8900.0 0.132 -17.588
9000.0 0.130 -17.702
9100.0 0.128 -17.870
9200.0 0.125 -18.052
9300.0 0.122 -18.279
9400.0 0.120 -18.418
9500.0 0.119 -18.510
9600.0 0.121 -18.365
9700.0 0.113 -18.951
9800.0 0.111 -19.100
9900.0 0.115 -18.813
10000 0.104 -19.625

I've tried doing some research but can't seem to grasp what "Vrms" means. I looked here and am still confused as to what this means in regards to pickups:

www.apogeeweb.net/tools/rms-voltage-calculator.html

I can understand that dBV means amplitude at a particular test frequency, and I can understand that on the plot picture, the "dV: 3.0dB" means there's a 3.0dB difference between the 100Hz baseline and the resonant frequency, which is 1800Hz.

And I can see that represented in the numbers: the numbers show that the dBV is almost exactly 3.0 higher at 1800Hz compared to 100Hz. So I could deduce "3.0dB @ 1800kHz" based on these numbers in the data alone.

But again, what about Vrms? I have no idea what to do with that number or what that's telling me. I do notice that it's highest at the resonant frequency, which would make me think, in layman's terms, it's a measure of voltage at a particular frequency.

But it's not a metric I see represented graphically on the bode plot, where I only see dBV and frequency. Any help understanding this would be appreciated.

[JohnH]

I get the concepts enough, but there's some details about common audio/electronic conventions for decibels that I'm not fully clear on

V RMS is the voltage coming out of the pickup in this test, as if it was measured on a meter, and also, what you would see on an oscilloscope. RMS refers to a method of averaging through an AC cycle with respect to power, and for a single AC signal, RMS is 1/sq root 2 of the peak. So an ac signal V RMS of say 2V into some load, would develop the same power as 2V dc. The peak voltage of this 2V RMS signal would be 2.82V.

But audio sounds, and also the electrical signals that generate them, are often expressed on a Decibel dB scale, and its a logarithmic scale of power because that is how sound is most closely experienced, and its compact across a wide range of levels. So doubling of power is always +3db.

dBs are a ratio between two levels of power, Formula: dB = 10 log10(Power1/Power2). The "+3db = double" is strictly 10Log10(2) = +3.01db

Anytime you listen to a sound, and double its power, it adds +3dB and it sounds like one quite small equal step up in volume.


Are we having fun yet?


Now back to the charts and data. Because dB's are based on a ratio, you have to have a reference. In the chart and data, it looks like they take a level of 1V RMS as the reference. And now there's another wrinkle that needs to be added. dBs refer to power, but the data refers to voltage. If you use these signals to create some power i a fixed load, the power will be dependent on voltage squared. So double the power is +3dB but double a voltage, you get 4x the power and its +6dB.

The formular changes to dBV (note the added V) = 20Log10 (V1/Vref) and Vref is 1V by convention.

So now, the measured voltage of 2.16V RMS, as compared to a reference of 1V RMS, is 20Log2.16 = 6.69 dBV and this is as tabulated for100hZ

At the resonance, the voltage is 3.04 V RMS leading to 9.66 dBV by the same method

So you see a rise of about +3dBV between these levels. And if you took that response and blasted it through an amplifier, all the power levels would go up but the ratio would stay the same and there would still be 3dB between the peak and the low frequencies.

Does that help?



(Others please correct, simplify, clarify or complicate as you wish. or just agree / ignore)

J

[timtam]

Trying to cut things back to a bare minimum, I would explain it something like this (if my memory serves me) ...

The Vrms is what comes 'first' if you like. It is, as mentioned, the output voltage of the excited pickup - the raw signal that the USB oscilloscope software is actually measuring from the pickup. The fact that it is expressed as an 'rms' figure is kind of irrelevant - that's just a way of expressing the overall level of a varying (sine-wave) voltage, like an analog frequency signal. So no real need to dwell on the rms bit.

The dBV figure on the other hand is a calculated ratio - a way of expressing a voltage in relation to another (reference) voltage. Here the reference voltage is 1 Vrms. The formula to calculate dBV (that is, dB for voltage) is 20 log(Vout/Vin) [for power the calculation is a little different]. Here Vin is the reference (that is, 1 Vrms) and Vout is the measured output voltage, in Vrms. So here dBV = 20 log (Vrms).

If you put your columns of data into Excel and add a new column with the formula =20*LOG(B1) ... where B1 is the column with the Vrms values .. and then fill-down with that formula to fill the whole column, you will get the same number as in the dBV column.

So given that Vrms and dBV use the same data, they are just different ways of expressing the same basic result ... the frequency response of the pickup. If you plot the two curves you will see that they have a somewhat different shape though, by virtue of the fact that dBV is a log quantity. However their peaks are at the same frequency.

[aquin43]

Vrms is a way of solving the problem of giving one useful number representing a voltage that is varying in time, such as a sine wave or other audio signal. If you measure the average of the time varying voltage, you get zero because e.g. a sine wave spends as much time negative as positive. If you measure the peak, you get something that varies wildly with the waveform shape.

The answer to the problem is to consider the power that the signal would deliver to a resistive load. At any instant this will be Vsquared/R, which will always be positive. So we average Vsquared over the cycle and get a definite number representing the power. But it was the voltage that we wanted so we take the square root of this average power and we arrive at a number that represents the voltage. This is then the ROOT of the MEAN of the SQUARE - Vrms.

DeciBels measure the ratio between two powers P1 and P2 on a logarithmic scale - log(P2/P1) where the logs are base 10 logs as used in the log tables before we had calculators.  A Bel represents a power ratio of 10:1. The Bel was considered to large for practical use so the deciBel at a tenth of the size was introduced, 10dB to a Bel.

This makes a dB power measurement 10*log(P2/P1). Now, if you are measuring voltages at a point in a circuit, the power ratio between two voltages V1 and V2 goes as the square of the voltage ratio, so the dB measure would be 10*log(square of(V2/V1)). But, it is in the nature of logarithms that the log of a squared number is just twice the log of the number. So, the square can be replaced by a factor of two giving dB = 20*log(V2/V1).

DeciBels represent ratios, but a logarithmic scale is so useful that that would be valuable to be able to use dB as an absolute measure of level. All that is needed is to introduce a nominal reference level. We then have dBV, which are supposed to be referred to a 1Vrms level at the measurement point. Thus a signal voltage can be given as Vrms or dBV, whichever is the most useful at the time.

Note that dbV is an absolute measure. When comparing two dBV measures, the V should be dropped and the ratio should be given in in plain dB.

[guitarmd]

Thanks for the replies and explanations. Extremely helpful!