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I am trying to experiment a fm transmitter project of Raspberry Pi - with a frequency of 88.1 MHz.

http://icrobotics.co.uk/wiki/index.php/Turning_the_Raspberry_Pi_Into_an_FM_Transmitter

However, I am reading the specifications in my country -

https://gazette.govt.nz/notice/id/2010-go4604?year=2010&noticeNumber=4604

I can see that I can use the frequencies like

(1) The permitted transmitter carrier frequencies are:
87.6 MHz 87.7 MHz 87.8 MHz 87.9 MHz
88.0 MHz 88.1 MHz 88.2 MHz 88.3 MHz
106.7 MHz 106.8 MHz 106.9 MHz 107.0 MHz
107.1 MHz 107.2 MHz 107.3 MHz 107.4 MHz
107.5 MHz 107.6 MHz 107.7 MHz ''

However, I am unsure on the radiated power. How can I calculate in theory the radiated power from the FM broadcast antenna?

Also, how do I calculate the field strength in dBµV/m?

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However, I am unsure on the radiated power.

In the govt.nz document you linked it says: -

(3) The maximum radiated power shall not exceed 0 dBW (1 W) e.i.r.p.

(4) Notwithstanding the provisions of (3), the field strength shall not exceed 95 dBµV/m based on a measurement at a distance of 100 metres from the transmit antenna.

how do I calculate the field strength dBµV/m

The E field and H field associated with a transmission is the power per square metre. This is because the E field is volts per metre and the H field is amps per metre. Multiply them together to get watts per square metre.

However, there is a simplification: In radio transmissions through air/vacuum the E field is 377 times the H field due to the impedance of free space (377 ohms).

So, if the power per square metre is 1 mW then the E field will be: -

$$\sqrt{power \times 377} = 0.614 V/m$$

Using logarithms, 95 dBµV/m is 56.234 mV/m or 0.056234 V/m and is the same as an incident power density of 8.388 uW/sq metre.

How can I calculate in theory the radiated power from the fm broadcast antenna?

The Raspberry Pi transmitter that you linked would not be regarded as "legal" because it will also transmit harmonics of the carrier frequency and this will interfere with other radio broadcast bands probably well past 1 GHz. A proper (legal) transmitter will use tuned circuits to restrict out-of-band interference that it would otherwise generate should those tuned circuits not be present.

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