# Bandwidth and Data Rate FSK Demodulations

I have a question about the data-rate limitations imposed from bandwidth for FSK signals. Suppose I transmit an FSK signal with frequencies as:

$$f_1 = 2400 MHz,$$ and $$f_2 = 2401 MHz$$

that is detected by a receiver. Assuming that the DC output voltage of the detector in the receiver is 100 mVp for 2400 MHz and 110 mVp for 2401 MHz. Without focusing on the circuit design, Is there any limitation on the rate at which I can transmit and receive this signal correctly? I always hear that the bandwidth limits the data-rate but I don't understand exactly why.

Without focusing on the circuit design, Is there any limitation on the rate at which I can transmit and receive this signal correctly?

The detector may take some time to reach 0.11 volts from 0.10 volts - this may be nano seconds, tens of nano seconds or hundreds of nano seconds etc.. Given that you have proposed no detailed design, then you have to decide what that factor is and, if you change the data too fast you may have a scenario where the DC output is slewing (say) between 0.104 volts and 0.106 volts for a continuous stream of ones and zeros.

At this point you ask yourself if any occurrence of noise could force 0.104 volts to be closer to 0.106 volts and produce an error in the received bit-stream. Then you ask yourself what bit error rate you can tolerate.

• That's more implementation detail the question is seeking to avoid, than the theoretical linkage to bandwidth that the question is actually asking about. – Chris Stratton Jul 9 '19 at 14:03
• I am implying bandwidth when mentioning the detector speed. There are other areas where bandwidth plays a role but this should be enough to spark a little learning or understanding. – Andy aka Jul 9 '19 at 18:17
• Thank you for the comment. I am aware of the circuit limitations. But from a completely theoretical communication perspective and not an RF circuit designer, I keep hearing that bandwidth limits data rate. From this example, I cannot see how that is even possible. – user367640 Jul 10 '19 at 19:35
• I would also like to add, that I randomly selected those DC voltages. I could have selected 200 mV and 0 mV. I see what you are suggesting about the bit error rate. – user367640 Jul 10 '19 at 20:08
• Well, given a stream of bits perfectly encoded as FSK at infinite bandwidth I.e. instantaneous changes in frequency, if you run that signal through a limited bandwidth filter you’ll find that the output takes more than zero femto seconds to slew into a frequency change. That effectively means that the demodulator takes more than no-time to slew into a bit change. Just get a simulator and prove it to yourself if you don’t believe me. – Andy aka Jul 10 '19 at 22:06

If you are using an optimum receiver with carrier synchronization, there is indeed a relationship between frequency difference ($$\\Delta f = f_2 - f_1\$$) and the cross correlation factor ($$\\rho\$$) that determines the bit error rate for a given noise spectral density.

To put it simply, if $$\\rho = 1\$$ then the two signals are 100% related, a distinction in the receiver is not possible. An important special case is $$\\rho = 0\$$. Such signals are orthogonal, which means that they can be perfectly separated again. For FSK with a coherent receiver (with carrier synchronization), we have orthogonal signals if $$\\Delta f = \frac{1}{2\cdot T_S}\$$, where $$\T_S\$$ is the symbol duration (for binary FSK equal to the bit duration).

To cut a long story short: If the symbol duration is chosen too short, the cross-correlation factor goes towards 1 and the errors increase.

For a simple non-coherent receiver (without carrier synchronization), the condition for orthogonal signals is $$\\Delta f = \frac{1}{T_S}\$$.