25-08-2012, 10:57 PM
I realise that what follows is making a point that has already been adequately discussed and I would have made this post much earlier but for the simple reasons that (a) up to now my test bench has been totally cluttered with other work and (b) finding the time to do what follows has simply not been available. However, better late that never - and I hope what follows is of some value to this thread.
From the bottom of my test equipment storage rack, I dug out my Marconi TF 893A A.F. power meter and my Advance J2 A.F. sig. gen. For measurement of various a.c. voltages, I used my Tektronix 475 'scope. To measure resistance, I used my Fluke 77.
The J2 has an output that is stated as being of 5 Ω resistance: I decided to check this first. I set the J2 frequency to 440 Hz and by connecting a non-inductive variable resistance across the output of the J2 and monitoring the voltage across it with the 'scope, I determined that the J2's internal resistance was of the order of 4 Ω.
I set the 893A power meter to a Rin value of 5 Ω and trimmed the output of the J2 so that 100 mW was indicated on the power meter. (Just out of interest, when the Rin value of the power meter was changed to 4 Ω, the change in the power meter was virtually undetectable). The voltage across the power meter's input terminals (Rin) was 2v p/p = 0.7 v r.m.s.
I now introduced a variable, non-inductive resistance between the J2 and the power meter. When the voltage across the power meter's input terminals (Rin) was now 1v p/p = 0.35 v r.m.s, (i.e. half the magnitude of the previous measurement), the power meter indicated 24 mW (which is what we would expect of course: half the voltage in → quarter of power out to meter; O.K., 25 mW to be exact!).
I then removed and measured the value that variable resistance: it was 9 Ω.
And so to the arithmetic.
1. First part: prior to introducing the variable resistance.
We have: Vs / (4 + 5) = Vin / 5,
so: Vs / 9 = 0.7 / 5,
so: Vs = 1.26 v r.m.s.
2. Second part: having introduced the variable resistance.
We have: Vs / (9 + R) = 0.35 / 5, where R is the unknown variable resistance.
Since Vs is now known, we get:
1.26 / (9 + R) = 0.072,
and this yields a value of R = 8.5 Ω.
From the above, the measured value was 9 Ω.
Conclusion: measurement method and theory thus vindicated by a practical example. [The difference of 0.5 Ω (5.5%) is put down to intrinsic measurement error, tolerances of the measurement equipment and approximations in the arithmetic].
Al. / Aug. 25th., 2012 //
From the bottom of my test equipment storage rack, I dug out my Marconi TF 893A A.F. power meter and my Advance J2 A.F. sig. gen. For measurement of various a.c. voltages, I used my Tektronix 475 'scope. To measure resistance, I used my Fluke 77.
The J2 has an output that is stated as being of 5 Ω resistance: I decided to check this first. I set the J2 frequency to 440 Hz and by connecting a non-inductive variable resistance across the output of the J2 and monitoring the voltage across it with the 'scope, I determined that the J2's internal resistance was of the order of 4 Ω.
I set the 893A power meter to a Rin value of 5 Ω and trimmed the output of the J2 so that 100 mW was indicated on the power meter. (Just out of interest, when the Rin value of the power meter was changed to 4 Ω, the change in the power meter was virtually undetectable). The voltage across the power meter's input terminals (Rin) was 2v p/p = 0.7 v r.m.s.
I now introduced a variable, non-inductive resistance between the J2 and the power meter. When the voltage across the power meter's input terminals (Rin) was now 1v p/p = 0.35 v r.m.s, (i.e. half the magnitude of the previous measurement), the power meter indicated 24 mW (which is what we would expect of course: half the voltage in → quarter of power out to meter; O.K., 25 mW to be exact!).
I then removed and measured the value that variable resistance: it was 9 Ω.
And so to the arithmetic.
1. First part: prior to introducing the variable resistance.
We have: Vs / (4 + 5) = Vin / 5,
so: Vs / 9 = 0.7 / 5,
so: Vs = 1.26 v r.m.s.
2. Second part: having introduced the variable resistance.
We have: Vs / (9 + R) = 0.35 / 5, where R is the unknown variable resistance.
Since Vs is now known, we get:
1.26 / (9 + R) = 0.072,
and this yields a value of R = 8.5 Ω.
From the above, the measured value was 9 Ω.
Conclusion: measurement method and theory thus vindicated by a practical example. [The difference of 0.5 Ω (5.5%) is put down to intrinsic measurement error, tolerances of the measurement equipment and approximations in the arithmetic].
Al. / Aug. 25th., 2012 //
