## The sensitivity of a DAB-receiver

When a DAB+ transmitter (VHF Band III) transmits on a frequency of 200 MHz, the power of the transmission signal has already decreased by 98.45 dB after a distance of 10 km (a factor 0,000000000143 attenuation). From a transmitter with a capacity of 1000 Watts, only 0,00000014 Watt will arrive at the receiver after 10 km. That is a VERY SMALL POWER that will generate a VERY SMALL VOLTAGE at the receiver’s input!

You might think: “no problem, we can amplify this small voltage again and make it a bigger signal.” And indeed, electronics are capable of a lot. For example, we still receive signals from the “Voyager 1” today. A space vehicle launched on September 5, 1977, has left our solar system for quite some time. The “Voyager 1” signals take more than 20 minutes to reach earth. The device does have a satellite dish with a diameter of 3.7 m, which provides a considerable profit. But the spacecraft is mainly in “deep space, ” which is also a freezing place (almost absolute zero).

Why this story? Well, there’s a scientific snag here as far as receivers go:

ANY ELECTRONIC CIRCUIT GENERATES NOISE IF THE TEMPERATURE OF THE ELECTRONIC CIRCUIT IS HIGHER THAN ABSOLUTE ZERO (-273°C).

One can calculate this, but we want to save you this trouble. The NOISE FLOOR of an electronic circuit having a bandwidth of 1.5MHz (such as a DAB+ receiver) at ambient temperature is approximately -106 dBm.

The formula is:

Noise Floor [dBm] = 10 . LOG(KB . T . Bandwidth)

With KB, Boltzmann’s constant: 1.38E-23 [J/K]

and Bandwidth: 1.540 MHz (or 1.540E+6)

It is an important fact because it tells us the limit of the electronic system. No system can receive signals weaker than -106 dBm. Signals weaker than -106dBm will disappear in the noise generated by the receiver! So the input amplifier of the receiver has a fundamental problem due to the self-generated noise level.

If the amplifier shows twice the noise power at its output than at the input, it is said to have a noise factor of 2 (or a noise figure of 3dB). An amplifier with a noise figure of 2.5dB is the best of the best one can achieve at standard temperature (without cooling).

To keep the price of a DAB/DAB+ receiver economically viable, the average input stage of a DAB+ receiver has a noise figure of 6 to 7dB. In other words, the amplifier produces four times more noise at the output than at the input. It increases the theoretical minimum level of -106dBm to a new minimum of -100 dBm.

It means that the receiver is just beginning to see a signal of -100 dBm but cannot demodulate it yet. The DAB receiver needs a signal-to-noise ratio of a minimal 13 dB. Finally, it brings us to a practical level of -86 dBm to receive a signal strong enough to be demodulated without errors.

We can assume that -86 dBm will be about the theoretical sensitivity of a typical DAB+ receiver. It is the property of the DAB receiver. We will see in subsequent articles that there are still many external factors (external to the receiver) that can cause the receiver, even with this sensitivity, to have a hard time receiving radio signals.

Keep in mind:

• We define the receiver’s noise floor by the thermal agitation of the molecules in the electronic components and give a certain noise level per unit bandwidth.
• A noise figure is a number that indicates how much thermal noise power the first amplifier stage of a receiver will add to the received signal. The first amplifier is crucial.
• Modulation S/R is the difference between signal and noise power.
• The above three parameters determine a receiver’s sensitivity and theoretically amount to about -86 dBm for DAB+ receivers.
Better receivers can (for example) have a sensitivity of -90dBm and even more; worse receivers can, e.g., have a sensitivity of -82dBm and even less.

Radio broadcasters pay a lot of attention to coverage simulations. It shows them a nice coverage map of their transmitters. However, there is an unknown essential factor in those simulations because nobody ever asks themselves which receiver sensitivity the simulation has taken into account.

Most of the time, simulations use field strength. Maybe it is the correct way to express coverage. But this is a highly technical matter which often is challenging to understand. Conversion from field strength to power and further to receiver sensitivity is not an easy calculation.