Does higher frequency really cause more path loss?

This is the most common misconception in RF engineering. Free space does not attenuate radio waves differently at different frequencies. The apparent frequency dependence in the FSPL formula (FSPL proportional to f^2) arises because the formula assumes isotropic antennas, whose effective aperture shrinks as lambda^2. If you keep the physical antenna size constant (like a 1-meter dish), the receive antenna gain increases as f^2, exactly canceling the FSPL increase. A 1-meter dish at 30 GHz captures the same fraction of radiated power as it does at 3 GHz from the same distance. The frequency dependence in FSPL is an artifact of the isotropic reference, not a property of free space.

How do you use the Friis equation for a real link budget?

The Friis equation gives the received power in an ideal free-space link. A real link budget adds losses and margins: P_rx = EIRP + G_rx - FSPL - L_atmospheric - L_rain - L_cable - L_polarization - M_fade. EIRP = P_tx + G_tx - L_cable_tx. For a 5G NR base station at 3.5 GHz, 1 km range: EIRP = +46 + 18 - 1 = +63 dBm. FSPL = 32.4 + 20 log(3500) + 20 log(1) = 103.3 dB. Rain and atmospheric loss at 3.5 GHz: negligible. Cable loss RX: 1 dB. Fade margin: 10 dB. P_rx = 63 + 0 - 103.3 - 1 - 10 = minus 51.3 dBm. If receiver sensitivity is minus 95 dBm, the link margin is 43.7 dB.

What is EIRP and why is it used instead of transmit power?

Effective Isotropic Radiated Power (EIRP) is the product of the transmit power and the transmit antenna gain: EIRP = P_tx times G_tx. It represents the power that an isotropic antenna would need to radiate to produce the same signal strength in the direction of maximum gain. A transmitter with 1 watt (+30 dBm) and a 20 dBi antenna has EIRP = +50 dBm = 100 watts equivalent. EIRP is used because it captures the combined effect of transmitter power and antenna directionality in a single number. Regulatory limits are often specified in EIRP: FCC Part 15 limits WiFi at 5 GHz to +36 dBm EIRP, meaning you can trade transmit power for antenna gain as long as the product does not exceed the limit.

Propagation

Friis Equation

In 1946, Harald Friis published the equation that every RF link budget begins with. Transmit 1 watt at 2.4 GHz through a 6 dBi antenna toward a receiver 100 meters away with a 2 dBi antenna. How much power arrives? The Friis equation answers: P_rx = P_tx + G_tx + G_rx − FSPL. FSPL at 2.4 GHz, 100 m = 80 dB. So P_rx = +30 + 6 + 2 − 80 = −42 dBm. That single calculation tells you whether the link closes. Double the distance: add 6 dB loss. Double the frequency: add 6 dB loss (with isotropic antennas). The Friis equation is the starting point for every wireless system ever designed.

Category: Propagation

Published: 1946

Scaling: 6 dB per doubling of distance

The Most Important Equation in Wireless

Friis transmission equation (linear):
P_r = P_t G_t G_r (λ / 4πd)²

In dB form:
P_r(dBm) = P_t(dBm) + G_t(dBi) + G_r(dBi) − FSPL(dB)

Free-space path loss:
FSPL(dB) = 20·log(d) + 20·log(f) + 32.44
(d in km, f in MHz)

EIRP = P_t(dBm) + G_t(dBi) − L_cable(dB)

FSPL at Common Frequencies and Distances

Distance	900 MHz	2.4 GHz	5.8 GHz	28 GHz	77 GHz
10 m	51.5 dB	60.0 dB	67.7 dB	81.3 dB	90.1 dB
100 m	71.5 dB	80.0 dB	87.7 dB	101.3 dB	110.1 dB
1 km	91.5 dB	100.0 dB	107.7 dB	121.3 dB	130.1 dB
10 km	111.5 dB	120.0 dB	127.7 dB	141.3 dB	150.1 dB
100 km	131.5 dB	140.0 dB	147.7 dB	161.3 dB	170.1 dB

Common Questions

Frequently Asked Questions

Does higher frequency really cause more loss?

No. Free space does not attenuate differently by frequency. The apparent f² dependence in FSPL assumes isotropic antennas whose effective aperture shrinks with λ². Keep the physical antenna size constant and the receive gain increase cancels the FSPL increase exactly.

How to use for a real link?

P_rx = EIRP + G_rx − FSPL − atmospheric − rain − cable − fade margin. 5G BS at 3.5 GHz, 1 km: EIRP = +63 dBm, FSPL = 103.3 dB, margin = 10 dB, P_rx = −51.3 dBm vs. sensitivity −95 dBm = 43.7 dB margin.

What is EIRP?

Effective Isotropic Radiated Power = P_tx + G_tx. 1 W (+30 dBm) through 20 dBi antenna = +50 dBm EIRP = 100 W equivalent. FCC limits are in EIRP: you can trade power for gain as long as the product stays under the cap.

Related Terms

← Frequency Multiplier Gain Flatness →

Link Analysis

Free-Space Path Loss Calculator

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