Final answer:
To down-convert FM radio signals of 105.7 MHz and 106.7 MHz for an SDR limited to a 3.2 MHz sampling rate, a local oscillator with a frequency of 105.1 MHz can be used. This would create output carrier frequencies of 0.6 MHz and 1.6 MHz, both with bandwidths below 1.6 MHz. The block diagram for this down-converter includes input and output filters, a mixer, and a local oscillator.
Step-by-step explanation:
To design a down-converter for the given FM radio signals, you must create a block diagram that includes a mixer and a local oscillator. The task is to down-convert the carrier frequencies 105.7 MHz and 106.7 MHz into a range that can be sampled by an SDR with a maximum sampling rate of 3.2 MHz. The bandwidth of each FM station signal, due to frequency modulation, extends 0.020 MHz around the carrier, making the total bandwidth of interest up to 1.6 MHz.
The local oscillator frequency (fd) must be chosen so that it shifts both carrier frequencies into the required range without overlapping. For instance, if the local oscillator frequency is set to 105.1 MHz, then the output carrier frequencies after mixing would be:
- 105.7 MHz - 105.1 MHz = 0.6 MHz (for the first station)
- 106.7 MHz - 105.1 MHz = 1.6 MHz (for the second station)
The output signal bandwidth is guaranteed to be below 1.6 MHz because even the modulated signal of the second station, centered at 1.6 MHz with a modulation bandwidth of 0.020 MHz, will result in a signal band from 1.58 MHz to 1.62 MHz. This falls within the sampling capabilities of the SDR.
A block diagram for this down-converter would consist of:
- An input filter to limit the inbound frequencies to the range of interest.
- A mixer that combines the input signal with the local oscillator frequency.
- A local oscillator set to the chosen frequency (105.1 MHz in this example).
- An output filter to ensure that the down-converted signal is within the desired bandwidth.