THS720P measurement error with non sinusoidal waves

All,

Below is an interesting response plus an attached document that I received from the technical support folks at Tektronix that came as a final answer to my continued questioning about the Math channel inaccuracies of my TDS3034. Did you ever wonder why you couldn't make any sense of Bearden's and JLN's THS720P scope readings, well...........

Jon

Hi Jon,
Even though our scopes allow this it turns out the RMS measurement on a math waveform is bogus and has no value. I have a attached a document discussing this.

Best Regards
Jurgen Krannich
Tektronix Customer and Sales Support Center
email jurgen.r.krannich@tek.com
Phone - 503-627-3713 or 1-800-835-9433, ext.7 3713

8/20/97

There's a difference between WaveStar's True Power calculation and the way the THS720P's Harmonics FW does it. The difference can lead to
correlation questions.

First however, two important points should be be noted:

1. The classic formula for True Power i.e. (RMS volts X RMS current X Cos Theta)
   is VALID ONLY WHEN THE VOLTAGE AND CURRENT SIGNALS ARE PURE SINUSOIDS.

2. RMS values of power are meaningless - THERE'S NO SUCH THING AS RMS WATTS.

   By definition, power is, "The rate at which work is done".
   Mathematically, power is expressed as, "The derivative of
   work with respect to time" and is commonly measured in
   units such as Watts or Horsepower.

   Practically, the derivative of work may be defined as,
   "The instananeous rate of change of work with respect
   to a variable" (i.e. in electrical applications the
   variable is time).

   Further, power may also be defined as, "The rate per
   unit of time at which electrical energy is consumed or
   produced".

   The energy supplied by a current to a load (appliance)
   enables the load (appliance) to "work" or to provide other
   forms of energy such as light, heat, etc.

   The amount of electrical energy a load (appliance) uses is
   found by calculating the product of it's power rating
   (Watts) by the operating time. Units of electrical energy
   are usually expressed as Watt-Seconds (i.e. joules),
   Watt-Hours, or Kilowatt-Hours.

   Since electrically, RMS (i.e. root-mean-square) is defined
   as the, "The value of an AC current or voltage, equivalent
   to it's DC value, there is obviously no such quantity as
   RMS power (i.e. power is power - no equivalent).

WaveStar's "Measurement" function calculates several RMS power values
which, as shown above, are meaningless and should be ignored.
These include:

   RMS Watts
   AC RMS Watts
   Cycle RMS Watts
   Cycle AC RMS Watts

The correct way to calculate True Power is to perform an instantaneous
multiplication (i.e. point-by-point) to calculate the instantaneous
power waveform - then take the mean value of the power waveform.

In WaveStar, this is accomplished by:

   1. Acquire the voltage and current waveforms.

   2. Use the "Harmonics Graph" function to "Calculate Harmonic
Data".

   3. Use the "Harmonic Tabular" function and read "Power"
(above the table).

An alternate WaveStar method is to:

1. Acquire the voltage and current waveforms

2. Use the "Harmonics Graph" function to "Calculate Harmonic
   Data" and "Create Power Waveform"

3. Use the "Measurement" function and read "Mean (CH1*CH2)"

WaveStar performs it's calculations using floating point math and so, is quite accurate.

THS720P's Harmonics FW calculates True Power the same way but doesn't employ floating point math and so, truncates values. This leads to somewhat different answers.