Digital audio broadcasting system design and implementation

Analogue and Digital Converter

This is an electronic device that helps in the conversion of continuous signals to discrete or isolated digital numbers. When an analogue voltage or current is fed into the device as an input, it converts it into a digital number relative to the voltage or current magnitude. There are a number of terminologies related to ADC, which include resolution, accuracy, response type, sampling rate, aliasing, dither, oversampling, relative speed and precision, and the sliding scale principle, however, just a few of them will be considered in this study.

The resolution of an ADC refers to an indication of the isolated values that in can generate over the range of analogue values. Since the electronic storage of these values is in binary form the resolution is normally expressed in bits and the available discrete values being a power of two. For instance, an ADC whose resolution is 6 bits has the capability of encoding an analog input to one in 64 varied levels, given that 26=64. It is also possible to define resolution electrically and give the expression in volts. The voltage resolution of an ADC is found by dividing the overall voltage measurement range by the number of isolated intervals. The formula is written as:

Where:

Q= resolution in volts/step i.e. (volts/output codes-1)

EFSR= full scale voltage range which is given by VRefHi -- VRefLow

M= ADC's resolution in bits

N= number of intervals= 2M -- 1 (Knoll 1989)

Consider an example given by Knoll (1989) where the Full scale measurement range is 0 to 7 volts, the ADC resolution will be 3 bits which means 8 quantization level sie. 23. When this is given in terms of ADC voltage resolution it equals 7V/7 steps which give 1V/step.

The ADC is not exempted from errors that are encountered by other instruments and has errors that have a number of sources which brings about the question of accuracy. These errors are categorized as quantization error, non-linearity error and aperture error. Quantization error is caused by the finite resolution of the ADC and cannot be avoided in any ADC while non-linearity error occurs due to the physical imperfections of the ADC which leads to a deviation between the output and the input from a linear function. The third error is caused by a clock jitter and is usually exposed when digitizing a signal that is time variant. The non-linearity error can be toned down by calibration or eve averted by testing. In most ADCs the range of input values that map to every output value are linearly related to that output value and are referred to as linear ADCs.

The speed and precision of an ADC varies depending on the type of the ADC with the Wilkinson ADCs being considered the best since they exhibit the best differential non-linearity. ADCs are usually represented using a symbol; the conventional electrical symbol used is as below (schematic).

Demodulator (Band pass filter)

A band pass filter is a device that helps in the filtering of frequencies outside the required range, this it does by passing frequencies that are within a specified range and rejecting or attenuating those frequencies that are outside that range. A resistor-inductor-capacitor (RLC) circuit is an example of an analogue band-pass filter, it is also possible to create a band pass filter through bringing together a low pass filter and a high pass filter (Nicholson 1974). The actual fraction of the spectrum affected is referred to by the term passband and in a case where a band pass filter is ideal then this is completely flat which is to say that it has no gain throughout and would totally reject all frequencies that fall outside the passband. Practically, there is no ideal band pass filter since no filter attenuates all frequencies that lie outside the preferred frequency entirely, there exists a section just outside the wished-for passband where frequencies are not rejected but attenuated. This phenomenon is referred to as the filter roll-off generally expressed in Decibels of attenuation per octave of frequency. When a filter is designed there is the intention of making the roll-off as narrow as achievable which gives the filter a chance to get as close as possible to the intended design in terms of performance.

There is a difference that exists between the upper and the lower cutoff frequencies which is referred to as the bandwidth of the filter while the ratio of bandwidths which is obtained by using two distinct attenuation values in order to find the cutoff frequency is referred to as the shape factor. For instance, when the shape factor is said to be 2:1 at 30/3 dB then it means that the bandwidth obtained between frequencies at 30 dB attenuation is double that obtained at 3 dB attenuation. The electrical symbol of a band pass filter is as shown below (schematic).

According to Hasan (1991), the extensive test of the Phase Locked Loop (PLL) FM demodulator in Gaussian modulation is replicated in consideration of additive noise and FM interference by means of the Monte Carlo method. The modulating Gaussian random signals are simulated by sums of sine waves of equally spaced frequencies and random phases.

Monte Carlo simulation

By the Monte Carlo method, the Gaussian message ?s (t) of bandwidth Ws rad/s and rms frequency deviation ?s rad/s is simulated by a sum of Ns sine waves

(1)

Where is the peak frequency deviation of the nth tone, is the fundamental modulation frequency so that Ns

a = Ws, and is a random phase distributed uniformly over (-

). Analogously, the Gaussian message ?i (t) is simulated by (2)

Where, and Ni

a = Wi are, respectively, the peak frequency deviation of the nth tone, the rms frequency deviation and the bandwidth of ?i (t), and is a random phase distributed uniformly over (-

). If the numbers Ns and Ni of tones simulating the Gaussian messages are large enough, the statistics of (1) and (2) approach that of Gaussian noise.