Measuring the Ring Voltage on a Telephone

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— Clare Boothe Luce


Figure 1: Ringer For An Old Landline Phone.

Figure 1: Ringer For An Old Landline Phone (Source).

I received an email yesterday from a sales engineer who was having difficulty measuring the ring voltage on one of our telephone circuits. The numbers he was getting did not agree with what my engineering group had measured. The discrepancy had to do with the shape of the ring voltage waveform and what a standard voltmeter actually measures. As with many engineering problems, developing a practically useful solution depends on coming to an agreement on definitions and determining what the instruments are really measuring. This is a harder thing than one might think and this problem provides a nice illustration of basic problem solving.


Ring Voltage Specification

The ring voltage on a telephone is specified as a Root-Mean-Square (RMS) voltage. Electrical engineers like to use RMS voltages for varying waveforms because the RMS voltage can be thought of as the equivalent DC voltage with respect to producing power in the load. Many people think of RMS voltage as a form of "average" voltage, even though it really is the average of the square of the voltage.

The Wikipedia defines the RMS voltage of a periodic signal in terms of an integral (Equation 1).

Eq. 1 {V_{RMS}} = \sqrt {\frac{1}{T}\int\limits_0^T {v{{\left( t \right)}^2}dt} }

where T is the period of the signal and v(t) is the function that describes the waveform.

Ring Voltage Waveform

Figure 2 illustrates the ring voltage waveform that the sales engineer was dealing with. Trapezoidal waveforms in telephony are common.

Figure 1: Example of a Trapezoidal Telephone Ring Voltage

Figure 2: Example of a Trapezoidal Telephone Ring Voltage

The voltage waveform actually goes both positive and negative, but the polarity does not matter when calculating power into a resistive load. We will work here with the positive side.

Computing the RMS Voltage of a Trapezoidal Waveform

Equations 2-4 illustrate how to derive and expression for the RMS voltage of a trapezoidal waveform in terms of k and T, which are defined in Figure 2. This derivation assumes that the triangular portions of the trapezoid are identical.

Eq. 2 V_{RMS}^2 = \frac{1}{T}\int\limits_0^T {v{{\left( t \right)}^2}dt} = \frac{2}{T} \cdot \int\limits_0^k {{{\left( {\frac{{A \cdot t}}{k}} \right)}^2}dt} + \frac{1}{T} \cdot \int\limits_0^{T - 2 \cdot k} {{A^2}dt}
Eq. 3 V_{RMS}^2 = 2 \cdot \frac{{{A^2} \cdot k}}{{3 \cdot T}} + \frac{{{A^2}}}{T} \cdot \left( {T - 2 \cdot k} \right) = {A^2} \cdot \left( {1 - \frac{4}{3} \cdot \frac{k}{T}} \right)
Eq. 4 {V_{RMS}} = A \cdot \sqrt {1 - \frac{4}{3} \cdot \frac{k}{T}}

Crest Factor

Just to complicate matters, the ring voltage is actually controlled by two specifications: an RMS voltage level and a Crest Factor (CF). CF is defined shown in Equation 5.

Eq. 5 CF \triangleq \frac{{\left| {\max \left( {v(t)} \right)} \right|}}{{{V_{RMS}}}}

CF is commonly used because many electronic devices are sensitive to peak-to-average ratios, which CF measures. Telephony specifications require that 1.2 ≤CF ≤ 1.6.

Correction Factor for a Peak Detecting Meter

While there are electronic voltmeters that measure true RMS voltages for any waveform, the sales engineer in this case is using an electronic voltmeter that assumes the operator is always measuring a sinusoidal signal. It measures the peak voltage of the voltage waveform and divides that value by the square root of 2, an approach which produces the correct RMS value for a sinusoidal waveform but not a trapezoid (see Equation 6).

Eq. 6 {V_{Meter}} = \frac{A}{{\sqrt 2 }}

Equations 7-8 show how to calculate a correction factor for adjusting the meters reading to give the RMS voltage for a trapezoid.

Eq. 7 {V_{RMS}} = \frac{{{V_{RMS}}}}{{\max \left( {\left| {v(t)} \right|} \right)}} \cdot \frac{{\max \left( {\left| {v(t)} \right|} \right)}}{{\sqrt 2 }}.\sqrt 2
Eq. 8 {V_{RMS}} = \frac{{{V_{Meter}}}}{{CF}} \cdot \sqrt 2

A Field Example

In this particular case, the field engineer was measuring 60 V for something that Engineering said was 65 V. We can summarize the critical variables as follows:

  • Trapezoid voltage peak voltage (A), is 86 V (set by the telephone ringer circuit design).
  • CF is 1.33 (set by Engineering in the firmware)
  • Value measured in the field, VMeter, is 60 V.

We can compute the correct RMS value by using Equation 8. This calculation is shown in Equation 9.

Eq. 9 {V_{RMS}} = \frac{{{V_{Meter}}}}{{CF}} \cdot \sqrt 2 \doteq 60{\text{ V}} \cdot \frac{{1.414}}{{1.333}} = 65{\text{ V}}

This shows that the result measured by the sales engineer and my engineering group were actually the same.

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15 Responses to Measuring the Ring Voltage on a Telephone

  1. Joel says:

    Finally something near and dear to my heart

    • mathscinotes says:

      There is something strangely satisfying about working on POTS stuff. The optics stuff is always difficult to write about because it gets very deep. The telephony stuff is much more "normal" analysis.

  2. Hamman says:

    My first time to visit your blog - I absolutely love it !

    I come from much of a same background as yourself - I have grown up in small town rural Ireland. I have had a deep passion for electronics since age five. This later developed into amateur radio, programming, science and engineering. Although I was bright at school - I too hated math and found it terrible hard work. I found it interesting but incredibly tricky and treacherous !

    My mother told me that you would need to be really good at math to studying anything electrical. This disheartened me - but I carried on. I worked hard at math-gradually becoming better.

    I am currently studying Electonics Engineering which now has a predominately has a software/firmware content. I selected Electronics Engineering in preference to Software Engineering as I did not want to be stuck at a PC writing code all day .
    Unfortunately for the most part- this is what Electronics Engineering has became.

    The analog that I know and love is only taught in the extreme basics. Graduates now have far less analog knowledge than 20 years ago. I am in my 3rd year ( doing my second last exam for the course in just over 3 hours from now!). I continue to work on analog projects in my own time ( currently developing a new unusual product which involves an analog multiplier- the reason I found your website ).

    I find the math that you detail here to be excellent - you lay it out nicely and its at a standard that (at least the majority of which) I can understand .
    It is with pleasure that I can now read engineering text and actually have a handle on what the maths are telling me.

    I admire people like you - my aspiration is to become as proficient you.

    Thank you for the wonderful blog - I will be a regualr from now on.

    Best Reguards,

    N.B I would also add to your list of analog gurus -Bob Wildar.

    • mathscinotes says:

      I hope things went well on your exam! Thank you for the kind comments. Like you, electronics has been a love since I first began building radios in grade school. I even did my graduate work in analog electronics. Good luck on your career.

  3. Pingback: Trapezoids Better Than Sinusoids? | Math Encounters Blog

  4. john says:

    i am into collecting restoring old telephones from wooden wall to rotary desktop phones. is there a way to make a analog WESTON a.c. voltage meter read the correct voltage at 20hz? it currently only read about 40 volts when i know it is about 90 volts @20hz. i was trying to see what my phone tester analyzer was putting out. also if i am testing my magnetos after i repair them will a cheap dvm read that a.c. correctly? i only have a high school education so please keep the answers to where i can research on my own.does the magneto hz vary with cranking speed?


    • mathscinotes says:

      i am into collecting restoring old telephones from wooden wall to rotary desktop phones. is there a way to make a analog WESTON a.c. voltage meter read the correct voltage at 20hz?

      We measure ringer voltages all the time using standard, calibrated, full-functional voltmeters. That said, I looked up the specifications for a Weston AC voltage meter at this web page. It states that

      Both ammeters and voltmeters may be used without appreciable frequency error over the whole range of commercial frequencies from 25 to 133 cycles per seconds.

      Assuming the meter is still good (a BIG assumption), your 20 Hz signal is slightly out of its frequency range. Normally, this would introduce a small error. In this case, it could be that the meter's capacitors have failed and it cannot function even down to its specified minimum.

      it currently only read about 40 volts when i know it is about 90 volts @20hz.
      How do you know that? I assume because it is ringing a phone. Remember that modern phones will ring down to 40 V RMS.

      i was trying to see what my phone tester analyzer was putting out. also if i am testing my magnetos after i repair them will a cheap dvm read that a.c. correctly? i only have a high school education so please keep the answers to where i can research on my own.does the magneto hz vary with cranking speed?

      The magneto voltage varies with cranking speed and load. Crank fast and those babies can put out enough voltage to really hurt! The following quote from this page may be of interest to you.

      Testing the magneto.

      After you have the magneto oiled, connect a meter to the outputs and turn the crank to see how much voltage you get. It should be 70 to 90 AC volts for a fairly fast crank speed. If it's less than that, like about 35 to 45 volts, which is highly likely in the 100 year old ones, it will not have enough power to drive the ringer, and there is no fixing the magneto. The voltage output depends on how strong the magnetic field is in the bar magnets which compose the stator.

      It is possible that your meter is okay and ringer's stator magnets have become weak over time. It is interesting that your voltage reading is the same as mentioned in the quote. Of course, both meter and the magneto could be defective.


      Don't let your let your lack of post-high school education stop you from doing anything. My father was one of the smartest people I have ever met and he never got past 10th grade.

      • john says:

        i put one of my new never used magnetos on the weston and it read 90 v.a.c. got it up past 100 when turning fast so it looks like it will work for what i wanted after all.i love analog meters because once you learn what position the needle should be at for a normal reading you can just look at it without having to know the number or make a line on the face for a minimum reading.i put my cheap dvm back on my phone anaylzer and this time it showed 85 v.a.c. if some has suspected weak magnet on their ringer maget for a old wooden wall phone you can put a rare earth magnet[aspirin size] on the bottom side right above the clapper bar. try it both ways because it helps a little with poles one way and a lot the other way. i brought a ringer back to life that was barely wiggling this way. going to experiment with rare earth magets on weak horseshoe magnets for the magnetos in the future will let you know how it worked out. you can watch som e of my videos on youtube at thanks for your reply sometimes a little help and info can lead you a long way down the path of learning.

  5. john says:

    the WESTON meter is a model 433. a friend of mine had it and gave it to me for my magnetos.

    • mathscinotes says:

      The Weston 433 has the following accuracy specifications (Source):
      Weston, Model 433
      Ac volts
      Range: 0 to 750 V
      (horizontal position)
      0.75% of FS, 25 to 125 Hz
      1.25% of FS, 125 to 2500 Hz

      As you can see, it also is specified to work to 25 Hz.

  6. john says:

    i set the analyzer for 40 hz ringer voltage by changing the dip switches inside and tried the weston and it was only off by 8 volts compared to my digital multimeter. it appears that at the lower range of the hz specs it off but at household current at 60 hz it reads pretty close. must be some componets inside the meter out of tolerance. beyond my skill level for me to troubleshoot. anyway when hooked hooked to the magnetos it shows what i wanted so i should be good to go now.have to learn to check the specs on equipment to know how to use them properly.thanks for your replies and help!

    • mathscinotes says:

      Everything you are saying makes sense. The meter responses can reduce quite quickly outside of their specified frequency range. Your test approach was exactly what I would ask of one of my engineers. Good troubleshooting work!


  7. john says:

    my weston has three posts on the side side and has a 0-150 range and a 0-15 v.a.c. range. broken leather handle/strap on top but i may fabricate a new one for it. thanks again.

  8. Pingback: Measuring Telephone Ring Power | Math Encounters Blog

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