Radio Frequency (RF) Carrier Signal

As mentioned above, a carrier sinusoid carries the information signal over the airwaves in the case of radio transmission or though wires or optical fibres in the case of telephony or computer communication.

The carrier for radio is a sinusoid with a high frequency. For example, the carrier frequency for FM signals will be around 100 MHz which means that the transmitter will produce a sinewave which goes through one cycle 100,000,000 times per second, or one cycle lasts for a period of 10 nanoseconds (ns) which is 10 billionths of a second. A DAB carrier frequency will be around 200 MHz (for its present use in band III) so would have a period of 5ns because the frequency is the reciprocal of the period and vice versa, i.e.:

frequency = 1 / period

The carrier “carries” the information by being modulated by an information signal such as an audio signal. Modulation just means “is modified in some way”. The easiest way to describe modulation is using the example of amplitude modulation (AM). Here, the audio signal will alter the amplitude of the carrier; when the amplitude of the audio signal goes up, the amplitude of the carrier goes up too by a proportional amount, when the signal goes down, the carrier frequency goes down, and so on. For frequency modulaton (FM), the amplitude of the audio signal changes the frequency of the carrier so that when the amplitude of the audio signal goes up, the carrier frequency will be increased to a higher frequency and when it does down the carrier frequency will go down. Another type of modulation is phase modulation. Here the phase angle of the carrier is changed. This is more important for digital modulation and will be dealt with later.

The audio signal is called a baseband signal or lowpass signal because its band of frequencies go down to zero frequency, or DC (direct current) or to a low frequency  relative to high frequencies such as radio frequencies. For example, audio signals cover the range of frequencies from 20Hz up to 20kHz and so as this band of frequencies is very low in comparison with the radio frequency (RF) carrier the audio signal is termed a baseband- or lowpass-signal.

The result of modulating the carrier with the baseband signal is that the band of frequencies (spectrum) of the baseband signal is translated up to the carrier frequency, hence another name for this is upconversion. One thing that confuses people not familiar with communication theory is that as a result of using Fourier Theory, the signal contains negative as well as positive frequencies.  Don’t bother trying to visualize what negative frequency really means in the physical world and just accept that a signal such as an audio signal is analyzed in the frequency domain using both positive and negative frequencies components and an audio signal’s negative frequency components are the mirror image of the positive frequency components, mirrored around zero Hz, so the spectrum looks symmetrical and the symmetric axis is 0 Hz. The effect of translating this baseband spectrum up in frequency though is that both the positive and negative frequency components are translated up in frequency. For example, if you just multiplied the carrier frequency with a frequency of 100 MHz by a baseband signal, this translates the baseband signal up in frequency so that the upconverted signal’s spectrum now is symmetrical about the carrier frequency at 100 MHz. So, if you had a baseband signal with a bandwidth of 20kHz and upconverted this signal by multiplying it by the carrier, the new spectrum at the higher frequency will cover the frequency range 

f_high = 100 MHz + 20kHz = 100.02 MHz

down to

f_low = 100 MHz – 20 kHz = 99.98 MHz

so its bandwidth is:

B = f_high  -  f_low  = 100.02 MHz  -  99.98  MHz  =  40 kHz

That is, because both the positive and negative frequency components have been translated up in frequency the baseband bandwidth has doubled from the original 20 kHz to 40 kHz.

This higher frequency signal is called a passband signal as opposed to a baseband signal.

Radio signals are often converted first up to an intermediate frequency (IF), before being converted higher to the radio frequency (RF). This is to do with filters being easier to build with a given frequency response when the filter has a fixed centre frequency than are filters that have a variable centre frequency. The centre frequency is halfway between the filter’s upper and lower cutoff frequencies and a cutoff frequency is where the frequency outputs a frequency component with half the power that it contained at the filter input.

As well as at the IF, there will be a filter at the higher RF, which is the final transmitter centre frequency. This filter is used to limit the amount of power that strays into adjacent frequency bands and thus interfere with signals in the adjacent bands.