Example Data Table
| Case |
Power |
Deviation |
Audio Frequency |
Modulation Index |
Carson Bandwidth |
| Broadcast FM |
100 W |
75 kHz |
15 kHz |
5 |
180 kHz |
| Narrowband voice |
25 W |
2.5 kHz |
3 kHz |
0.833 |
11 kHz |
| Lab signal |
1 W |
5 kHz |
1 kHz |
5 |
12 kHz |
Formula Used
Power from peak voltage: P = Vpeak² / 2R
Power from RMS voltage: P = Vrms² / R
FM modulation index: β = Δf / fm
Carson bandwidth: BW = 2 × (Δf + fm)
Carrier component power: Pc = Pt × J0(β)²
Nth sideband pair power: Pn = 2 × Pt × Jn(β)²
EIRP: EIRP = Pt × 10^((Gain dBi − Loss dB) / 10)
ERP: ERP = Pt × 10^((Gain dBi − 2.15 − Loss dB) / 10)
How to Use This Calculator
Select direct power when transmitter output power is known.
Select voltage mode when RF voltage and load resistance are known.
Enter carrier frequency, deviation, and modulating frequency.
Use multiplier factor when deviation is increased by frequency stages.
Set sideband order high enough to show useful power spread.
Add feed line, filter, connector, and antenna values.
Press calculate. Review results above the input form.
Use CSV or PDF buttons to save the calculation.
Understanding FM Signal Power
FM transmission keeps total RF power nearly constant. The audio message changes frequency, not the carrier amplitude. This makes FM useful in noisy radio paths. Noise often appears as unwanted amplitude change. A limiter can reduce that error before demodulation.
What The Calculator Measures
This calculator starts with transmitter power or RF voltage. It then finds the modulation index from deviation and modulating frequency. The modulation index controls how power spreads around the carrier. A small index keeps most power near the carrier. A large index moves more power into sidebands.
Carrier And Sideband Behavior
The carrier component is not always the largest part. Its value follows the Bessel coefficient J0. Each sideband pair follows another coefficient, Jn. The total of all carrier and sideband parts equals the ideal FM power. This is why raising deviation changes spectrum shape, not total power.
Bandwidth Planning
The calculator also estimates occupied bandwidth with Carson’s rule. This rule is widely used for planning. It adds peak deviation and highest audio frequency. Then it doubles that sum. The result gives a practical bandwidth estimate. Real signals may need more space when audio processing is aggressive.
Field Power Estimates
A transmitter output is not the same as radiated power. Feed line loss, connector loss, filter loss, and antenna gain change the final field strength. EIRP compares the system to an isotropic radiator. ERP compares it to a half wave dipole. Both are useful in coverage work.
Why Results Matter
Power calculations help engineers choose safe levels. They also help students understand FM spectra. A sideband table shows where energy appears. This is useful for labs, licensing notes, and design records. It can also reveal when deviation is too high.
Best Practice
Use realistic load resistance and measured RF voltage. Enter the highest modulating frequency for bandwidth. Enter final deviation after any multiplier stages. Check sideband order until cumulative power is close to total power. Save the CSV or PDF result for later comparison.
Common Checks
Review every input before trusting the answer. Very small audio frequency creates a large index. High loss can erase antenna gain. Compare EIRP and ERP when reports use different standards. This prevents reporting mistakes during review.
FAQs
What is FM signal power?
FM signal power is the total RF power delivered by the transmitter. In ideal FM, modulation changes frequency, not amplitude. So total power remains nearly constant while energy moves between carrier and sidebands.
Does modulation index increase total FM power?
No. In ideal FM, modulation index changes power distribution only. Higher deviation creates stronger sidebands and a weaker carrier component. The total transmitted power remains almost the same.
Why does the carrier power change in FM?
The carrier component follows the Bessel coefficient J0. At some modulation index values, J0 becomes small. The missing carrier energy appears in sidebands, not as lost transmitted power.
What is Carson bandwidth?
Carson bandwidth estimates the practical occupied bandwidth of an FM signal. It is twice the sum of peak frequency deviation and highest modulating frequency. It is useful for channel planning.
What is sideband pair power?
Sideband pair power is the combined power in the upper and lower sidebands of the same order. Each pair is calculated with the matching Bessel coefficient and total FM power.
What is the difference between ERP and EIRP?
EIRP uses an isotropic radiator as the reference. ERP uses a half wave dipole as the reference. For the same system, ERP is usually 2.15 dB lower than EIRP.
Can I use RMS voltage for RF power?
Yes. Select RMS voltage mode when your measurement is RMS. The calculator uses P = Vrms² / R. Use peak voltage mode only when the entered voltage is a peak value.
Why should I export the result?
CSV and PDF exports help keep records for lab reports, radio design checks, and licensing notes. They also make it easier to compare different deviation and antenna settings.