# GSM/GPRS reach for Class 4 2W 900MHz/ Class 1 1W 1800Mhz

I'm studying differents GSM/GPRS modules and all of them have two operation modes depending the frecuency (900MHz and 1800Mhz). If I'm not wrong, for the same power higher frecuencies have a lower reach and higher trassmision rate than lower frecuencies.

My question is, how can I know the reach in meters of each range for a power of 2W or 33dBm in 900MHz and 1W or 30dBm in 1800MHz.

• Sorry, I forgot write it... The question is for ideal conditions. Thanks! – ferdepe Jan 4 '16 at 13:21

If I'm not wrong, for the same power higher frecuencies have a lower reach

Irrespective of frequency, the power radiated from an antenna is the same (if the power input to that antenna is constant). This means that at some arbitrary distance from a transmitting antenna, the same power density is present (watts per square metre) irrespective of frequency.

However, because a receiving antenna has a size that is dependent on wavelength, the effective area is becomes smaller with an increase in frequency. The bottom line is that the antenna receives less power and produces a smaller signal as frequency rises.

Sorry, I forgot write it... The question is for ideal conditions.

The formula that I use for the free-field assessment of link loss (power loss between transmit and receive antennas) is based on the Friis formula: -

Link Loss (dB) = 32.4 + 20$log_{10}$(F) + 20$log_{10}$(d)

where F is MHz and d is distance between the two antennas (kilometres).

If "F" were 2 (implying a doubling of operating frequency) the loss part of the equation would increase by 6.02 dB.

My question is, how can I know the reach in meters of each range for a power of 2W or 33dBm in 900MHz and 1W or 30dBm in 1800MHz.

To know how far you can get ideally in free-space you need to have a figure for the data rate you transmit at. If the data rate is really low you can design a receiver that has a very tight band-pass filter that excludes a lot of noise - this allows you to receive a signal that is much smaller and therefore distance can increase. Anyway the rule of thumb equation is this: -

Power required by receive antenna in dBm is -154dBm + 10$log_{10}$(data rate) dBm

So now you have an estimate of the power you need at the receiver based on data rate, a formula that describes how power is attenuated in free-space (link-loss) and you have your output power (1 or 2 watts). All you need to do is combine this lot together to get an estimate. On the good side, the gain (dBi) of the sending and receiving antennas makes the link-loss smaller. On the down side, operating conditions can vastly increase the link-loss both statically and dynamically. In fact this is a big subject and has spawned several different mathematical models by cellular handset companies and other interested parties.

The most basic form this takes is to say that link-loss will be at least 20 dB worse than the free-space model - the 20 dB factor is called Fade margin. There is also another commonly used models for link loss here. This is the Hata model for open areas: -

where

• LO = Path loss in open area. Unit: decibel (dB)
• LU = Path loss in urban areas for small sized city. Unit: decibel (dB)
• f = Frequency of transmission. Unit: Megahertz (MHz).

There is also the Okumura model for urban areas: -

where,

L = The median path loss. Unit: Decibel (dB)

LFSL = The free space loss. Unit: decibel (dB)

AMU = Median attenuation. Unit: decibel (dB)

HMG = Mobile station antenna height gain factor.

HBG = Base station antenna height gain factor.

Kcorrection = Correction factor gain (such as type of environment, water surfaces, isolated obstacle etc.)

You also might be interested in this website for estimating range. There is also this calculator.