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The following is a tutorial question from my teacher.

A transmitter requires the IM3 products to be -65dB below the main tones when the total output power is 20 dBm. Calculate the output IP3 of this transmitter.

This is what I think.

The output IP3 is the third-order intercept point, which is the input power level at which the third-order intermodulation distortion (IM3) products are 30 dB below the main tones. In this case, the IM3 products are -65 dB below the main tones,

$$OIP3[dBm] = P1 [dBm] + \frac{\Delta P [dBc]} {2} = 62.5 dBm$$

$$OIP3 = 30dBm + \frac{65 dB} {2} = 62.5 dBm$$

But the book give me 49.5 \$dBm\$.

SamGibson
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kile
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1 Answers1

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You have made several errors, not all of which contribute to your wrong answer

The output IP3 is the third-order intercept point, which is the input power level at which the third-order intermodulation distortion (IM3) products are 30 dB below the main tones.

The output IP3 is the power level at which an IM3 component is equal to one of the main signals, not 30 dB below.

It's worth correcting this, even though it doesn't contribute to your error, as you then give the correct formula for IP3

$$OIP3[dBm] = P1 [dBm] + \frac{\Delta P [dBc]} {2} = 62.5 dBm$$

Having given the correct formula, when you evaluate it, 30 dBm creeps in again instead of the actual P1, which for two equal tones with a total power of 20 dBm is 17 dBm.

Using the correct P1 gives the book answer

$$OIP3 = 17dBm + \frac{65 dB} {2} = 49.5 dBm$$

Neil_UK
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  • Where does 17dBm come from? Any formula for this? – kile Jan 09 '24 at 08:53
  • @kile The question gives you the total output power as +20dBm. It consists of two tones of equal power (plus some distortion products of insignificant power), so each tone is half the power of the total, or 3dB less, which is 17 dBm. – Neil_UK Jan 09 '24 at 09:37
  • Thank you for your explanation, but how do you know there is only two tones? The question doesn't say it's only two tones – kile Jan 09 '24 at 09:43
  • @kile That's from the context of an IP3 measurement, the standard test uses only two tones. There's also the detail that the IP3 is extrapolated from the behaviour at lower powers, we don't actually take the power output up to where the IM3 power equals the main tone power. Check out wikipedia, the second bullet point of 'definitions' states two tones. Multi-tone tests can be done, to characterise the wideband comms we get these days, but they are more recent. Where did you get all those 30's from? Is it because 1 watt is +30 dBm? – Neil_UK Jan 09 '24 at 12:08