And REACTANCE is imaginary.
But resistance does 'work'. A resistor 'dissipates' heat when powered. Examples are a 'Bar Heater' - 1 to 2kWatts. A fan heater or a hair dryer. Some of which can be used as a 'heat gun'!
Right now the 'issue' is how to measure power. My long time friend and fellow radio amateur wanted to 'calibrate' a transceiver to S9. What is S9 you ask? Well the convention amongst amateurs is S9 is equivalent to 50 micro volts. Where? At the receiver input. Usually assumed to be 50 Ohms. But it doesn't have to be so low...
Like a lot of signal generators the output level is around zero dBm. Oh sorry! That is 1 milli Watt into 50 Ohms. (even worse!) What is that in Volts? Time to get the calculator out.
Power = ( V (r.m.s.)^2) / R [That is V squared - and r.m.s. because this is an a.c. wave not d.c.]
which when transposed gives Power * R = ( V r.m.s. ^2)
Or V r.m.s. = SQR( Power * R) [ SQR mean the square root - see a spreadsheet program/app]
When I worked it out I was gratified to get the same figure as I remember from a long time ago! The SQR of (50 * .001) is 0.2236 volts r.m.s. So the ratio of S9 (50uV) to 0.2236 is 4472...
So how do you get to 50uV from a signal at .2236 Volts? You use an attenuator.
But his signal generator only had four 20 dB switched attenuators on the output. At this point we MUST discuss the use of dBV. This is because of the use of decibels and a constant impedance/resistance circuit. It is a 'convention' that radio frequency measurements in general use a input and output impedance of 50 Ohms. It didn't used to be... in the early days (last century) measurements at audio frequencies were done at 600 Ohms (in/out).
A voltage ratio of 4472 in dBV is 20 * log10( 4472) which is :- 73.0 dBV Which of course is impossible to achieve with his switched attenuator. He can get to 60 or 80 dB below the output...
So he needs a smaller step switched attenuator... Maybe a 1, 2, 4, 8 dBV attenuator?
Having got to this point I remembered that I had made a switched version many years ago using small toggle switches and resistors. Finding it was no problem. Drawing the circuit - no problem. Calculating the resistor values - time to hit the books. No not the Internet.
Miniature Toggle Switch Version [Circa 1980]
Well the original was calculated using the Handbook by Scroggie and a new scientific calculator. Using Pi type attenuators at 50 Ohms. I tested it on a Spectrum Analyser and it was certainly 'good enough' for h.f. and above. Might not be accurate at 400 MHz or higher. But if made today with surface mount components might just be accurate.
The calculated values Nearest standard value
Loss Shunt R Series R
1 dB 869.549 5.769 820 5.6
2 dB 436.211 11.615 470 12
4 dB 220.971 23.848 220 22
8 dB 116.143 52.844 120 51
Yes I know not very accurate - but close enough for Radio Amateur use. If you really - really want to - you could test a hundred of the standard values to find a close value. The sort of task given to students and apprentices last century. Oh and the 10 Ohm resistor? Well it is actually two in parallel. As I couldn't find a 5.6 Ohm resistor.
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