RF question that I have not found anywhere

Why is it when you lower the bandwidth of a transmitter on a given frequency will in turn increase your range of a receiver's ability to receive that signal? I understand that a smaller bandwidth gives the ability to have a antenna with a better gain for a tighter tolerance and passive components. Why is it that if I just send data at 1KHz compared to 100KHz, I get a longer range that the receiver can pick up the data?

It's not about the antenna. It is about receiver noise floor that depends on the bandwidth of the receive channel.

Signal to Noise Ratio SNR :: Radio-Electronics.Com

Strictly spoken, it's not the bandwidth rather than the signal rate (both are closely related with most modulation schemes however). You can achieve good SNR with large bandwitdh spread spectrum signals as well, as long as the signal rate is low.

FVM,
What do you mean by saying "as long as the signal rate is low"?

---------- Post added at 22:43 ---------- Previous post was at 22:37 ----------

volker_muehlhaus,
I have read your link. Correct me if I'm wrong. Just because I lower the bandwidth on the receivers end, I increase my SNR. If i'm using a SI4432 transceiver on both ends for transmit and receive, just by in software by lowering the data rate to a very low value, I will increase the SNR even though I only slowed the data rate?

Receiver sensitivity is given by:

Receiver.Sensitivity(dBm) = –174 + 10*LOG[Bandwidth(Hz)] + Receiver.NF(dB) + SNR(dB)

As you see from the equation, you have three choices to make receiver sensitivity better:
to narrow the bandwidth, to decrease the NF, or to decrease the SNR requirement.

Related exactly to your question, always the receiver bandwidth should follow the transmitter bandwidth.

Now you are referring to a specific chip and modulation scheme. That's different from talking about bandwidth in communication generally. For the general relation of date rate, bandwidth and noise, you can refer to the Shannon-Hartley theorem. Shannon

Looking at simple digital modulation schemes, particularly FSK derivates, there's already a relation between data rate and signal bandwidth involved. You have FSK separation as second independent parameter, but it's usually set to an optimal value according to the data rate (with some variations according to channel spacing and regulations).

The transceiver datasheets from Silabs and other manufacturers give typical numbers for receiver sensitivity versus data rate. As far as I'm aware of, they also assume an optimized IF setting for the receiver. I didn't comparative tests on my own, but I assume that the IF bandwitdh is in fact only part of the effective receiver bandwidth, because the digital demodulator filters the signal too and does the major part in establishing the real receiver bandwidth.

The analog input circuit and programmed IF bandwidth are important in two regards:

- it must not be below the signal bandwidth to avoid signal loss
- it plays a role in neighbour channel supression

P.S.: I have to correct my previous statement with regard to vfone's post. The given definition of SNR applies to wideband modulation schemes like spread spectrum as well. They can't increase the SNR but are lowering the SNR requirement by utilizing signal redundancy.

It's because the Receiver sensitivity improved.

What is receiver sensitivity?

The Minimum Detectable Signal(MDS) power, Pi(min) at which a receiver can detect a signal, while providing an adequate SNRo(min) at analog receiver output or BER at digital receiver output, for demodulation is called receiver sensitivity.

vfone's formula is right:
Receiver.Sensitivity(dBm) = ?174 + 10*LOG[Bandwidth(Hz)] + Receiver.NF(dB) + SNR(dB)

the 'Bandwidth' means signal's bandwidth.

For a receiver, the NF and SNR are constants. Narrow bandwidth will reduce the power of thermal noise. Noise reduced, and the SNR is constant, so the Minimum Detectable Signal power reduced accordingly.

From the history of "wireless" communication, engineers learned that to separate selected signals from other signals and noise and interference, one (and for long time the best ) way is to use resonance. Resonant circuits and filters made of them allowed to arrange a window in frequency domain, to pass a wanted signal while other signals and noise was attenuated.
Later it turned out that the thermal noise defined the lower limit of signal power at receiver input; by adjusting the width of the frequency window, the noise can be reduced till signal becomes distorted due to affecting its spectrum.
In conclusion, signal spectrum to be transmitted (defined by data rate and modulation mode) should be "matched" to fit the filtering window; this reduces the noise and optimizes the signal-to-noise ratio defining receiver sensitivity.
Modern UWB systems operate in another mode- instead of resonance, wideband signal processing is used to separate a wanted signal prom anything else. The correlation principle is used for it, which requires the sample of a wanted signal to be kept in the receiver for data retrieval.