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formula?
- Thread starter Lazybones1222
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This is going to be a fun thread.....<img src=http://www.ezboard.com/intl/aenglish/images/emoticons/tongue.gif ALT=":b"> I've spent more hours studying this topic than just about any other RF related (what's wrong with me???), and here's my current understanding. I'm sure I don't have it all yet, though.
RMS is a measurement of Electromotive Force (Volts) or Current (Amps), but not Power (Watts). Usually in RF when we use the RMS to Peak formulas, we're talking about Voltage. When people say they see 100 watts RMS, what you're really saying is that your meter is sampling the voltage and current, calculates RMS, and then converts and displays it as wattage on the meter. The formulas posted up earlier in this thread are all correct......but for converting voltage, not power.
Let's use an example: You're measuring a modulated AM signal using an RMS meter and you read 100 watts. (Forget about the carrier for now for simplicity) In order to find what the Peak power is, you can't multiply 100x1.414 because that formula applies to volts or amps, but not watts. So to figure it out, you have to convert 100 watts back to volts. In this example, if were assuming a purely resistive 50 ohm load, then we could use the forumula P=E^2/R (Ohm's law) to solve for volts (P=Watts, E = Volts, R = Resistance). You'll come up with 70.7 volts RMS. Now, you can multiply that times 1.414 to find Peak Voltage, which is 99.9 volts Peak. Ohm's law can be used to convert back to watts (P=99.9^2/50) and you'll get 199.9 watts Peak. You can pretty easily see that 199.9 watts peak is not equal to 100 watts RMS x1.414.
Another problem is that people confuse Average power (watts), Average volts, and RMS volts. They are not the same. In this case the following formulas apply:
Peak power (watts) = Average Power (watts) x 2
Average voltage = 0.637x peak voltage
Average voltage = .900 x RMS voltage
So now I think we have enough to get at what I think you're really asking: My Bird 43 reads 100 watts...how many watts peak is that? First, a Bird 43 says right on it that it reads CW power. CW power is the same as Average power, so the Bird 43 is not an "RMS Meter". The problem with trying to convert what a Bird 43 measures to Peak is that the meter is intended to measure average power for a carrier that is free of changing amplitude (that's what a CW signal is). However, AM and SSB are constantly changing in amplitude, so you can't just use the simple formulas above. Even if you give the Bird 43 a steady FOOOOOUUUURRRR into the mic, it doesn't have sensitive enough circuitry to give an accurate measurement of a voice pattern. Only if you gave the Bird a steady carrier or tone can you can calculate Peak power using the numbers it reports. What you CAN do is buy the Peak reading kit for the Bird 43. It adds the powered circuitry necessary to sample RF from a voice pattern and report Peak numbers. To get close with a stock Bird, you can just take the average power that it reports and double it (see formula above), but it's important to understand the error factor involved due to the sensitivity of the stock meter.
The original question was about how to calculate AM PEP. A pretty useful formula that I've found assuming you have a meter (or scope) than can show you modulation percentage is: PEP = ((Modulation factor + 1)^2)Carrier. If you have 100% modulation, then Modulation Factor = 1; 200% modulation is 2, etc.) So if you have a 25 watt carrier, you would have 100 watt PEP with 100% modulation (look familiar?). If you want to study more on this topic, here's a pretty good resource.
</p>Edited by: <A HREF=http://p067.ezboard.com/bworldwidecbradioclub.showUserPublicProfile?gid=moleculocdx363>MoleculoCDX363</A> at: 1/11/05 11:32 am
RMS is a measurement of Electromotive Force (Volts) or Current (Amps), but not Power (Watts). Usually in RF when we use the RMS to Peak formulas, we're talking about Voltage. When people say they see 100 watts RMS, what you're really saying is that your meter is sampling the voltage and current, calculates RMS, and then converts and displays it as wattage on the meter. The formulas posted up earlier in this thread are all correct......but for converting voltage, not power.
Let's use an example: You're measuring a modulated AM signal using an RMS meter and you read 100 watts. (Forget about the carrier for now for simplicity) In order to find what the Peak power is, you can't multiply 100x1.414 because that formula applies to volts or amps, but not watts. So to figure it out, you have to convert 100 watts back to volts. In this example, if were assuming a purely resistive 50 ohm load, then we could use the forumula P=E^2/R (Ohm's law) to solve for volts (P=Watts, E = Volts, R = Resistance). You'll come up with 70.7 volts RMS. Now, you can multiply that times 1.414 to find Peak Voltage, which is 99.9 volts Peak. Ohm's law can be used to convert back to watts (P=99.9^2/50) and you'll get 199.9 watts Peak. You can pretty easily see that 199.9 watts peak is not equal to 100 watts RMS x1.414.
Another problem is that people confuse Average power (watts), Average volts, and RMS volts. They are not the same. In this case the following formulas apply:
Peak power (watts) = Average Power (watts) x 2
Average voltage = 0.637x peak voltage
Average voltage = .900 x RMS voltage
So now I think we have enough to get at what I think you're really asking: My Bird 43 reads 100 watts...how many watts peak is that? First, a Bird 43 says right on it that it reads CW power. CW power is the same as Average power, so the Bird 43 is not an "RMS Meter". The problem with trying to convert what a Bird 43 measures to Peak is that the meter is intended to measure average power for a carrier that is free of changing amplitude (that's what a CW signal is). However, AM and SSB are constantly changing in amplitude, so you can't just use the simple formulas above. Even if you give the Bird 43 a steady FOOOOOUUUURRRR into the mic, it doesn't have sensitive enough circuitry to give an accurate measurement of a voice pattern. Only if you gave the Bird a steady carrier or tone can you can calculate Peak power using the numbers it reports. What you CAN do is buy the Peak reading kit for the Bird 43. It adds the powered circuitry necessary to sample RF from a voice pattern and report Peak numbers. To get close with a stock Bird, you can just take the average power that it reports and double it (see formula above), but it's important to understand the error factor involved due to the sensitivity of the stock meter.
The original question was about how to calculate AM PEP. A pretty useful formula that I've found assuming you have a meter (or scope) than can show you modulation percentage is: PEP = ((Modulation factor + 1)^2)Carrier. If you have 100% modulation, then Modulation Factor = 1; 200% modulation is 2, etc.) So if you have a 25 watt carrier, you would have 100 watt PEP with 100% modulation (look familiar?). If you want to study more on this topic, here's a pretty good resource.
</p>Edited by: <A HREF=http://p067.ezboard.com/bworldwidecbradioclub.showUserPublicProfile?gid=moleculocdx363>MoleculoCDX363</A> at: 1/11/05 11:32 am
QRN, right...I was about to make a follow up on the original question, which was on PEP.
As you were saying (I did it indirectly with the formula), PEP is a measurement of the modulation envelope, not a measurement an AC sine wave form. The formulas above converting RMS to peak are for AC sine wave form.
A note about the 375 watt AM rule of thumb for legal limit on ham bands: That also works for a pure sine wave modulating a carrier because the waveform is symmetrical. Because the human voice is assymetrical, it doesn't quite work perfectly. This is the part I'm still working on understanding completely. For now, I've been using this site reference as a guide to try to sort through it all. Maybe QRN has some pointers to help me out on this one.
Moleculo
</p>
As you were saying (I did it indirectly with the formula), PEP is a measurement of the modulation envelope, not a measurement an AC sine wave form. The formulas above converting RMS to peak are for AC sine wave form.
A note about the 375 watt AM rule of thumb for legal limit on ham bands: That also works for a pure sine wave modulating a carrier because the waveform is symmetrical. Because the human voice is assymetrical, it doesn't quite work perfectly. This is the part I'm still working on understanding completely. For now, I've been using this site reference as a guide to try to sort through it all. Maybe QRN has some pointers to help me out on this one.
Moleculo
</p>
A