Specifications
Sampling of the
Intermediate
Frequency
At the end of the test and reference Intermediate Frequency chains is an
18 bit ADC converter. Although this converter produces 18 bits on its out
-
put, its effective number of bits is approximately 15, meaning that it has
resolution up to 15 ideal bits. The ADC is a sampling converter, so it sam
-
ples then holds the input signal while the conversion takes place, thus
eliminating the need for an external sample and hold chip.
As mentioned earlier, the ADC samples 3 types of signals:
q
125 kHz sinusoid
q
453.125 kHz sinusoid
q
DC signal
The input signal range of the ADC is ± 2.75V, and the preceding Interme
-
diate Frequency chains ensure that signals at the ADC input are as close
to the full scale range as possible, thereby utilizing as much of the ADC’s
dynamic range as possible. The A/D sampling rate is fixed at 156.25 kHz,
which is clearly less than twice the 125 kHz and 453.125 kHz signals that
are input to the ADC. This under sampling technique allows the L.O. and
R.F. signals at the mixer to have more separation than the resulting
aliased signal produced by the sampling process.
Nyquist sampling theory states that a signal must be sampled at a fre-
quency greater than twice the highest frequency present in the signal, or
twice the bandwidth of the signal, in order to prevent aliasing. Aliasing
occurs when a high frequency signal takes on the alias of a lower fre-
quency signal after sampling. Aliasing results from the fact that, given a
fixed sampling frequency, samples of a cosine with frequency f are indis-
tinguishable (except for a phase change) from samples of a cosine with
frequencies (k*Fs+f),where Fs is the sampling frequency and k is a
fixed integer.
For example, cos(2*pi*f*t), becomes after sampling with period Ts,
cos(2*pi*f*n*Ts), where n is an integer. Since Ts = 1/Fs, the sampled sinu
-
soid can be expressed as cos(2*pi*f*n/Fs). Now, if the sinusoid’s frequency
is (k*Fs + f) before sampling, after sampling it becomes cos(2*pi*(k*Fs +
f)*n/Fs), which reduces to cos([2*pi*f*n/Fs] + 2*pi*k*n ). Since the cosine
function is periodic with period 2*pi, adding integer multiples of 2*pi to
the argument doesn’t change the value of the function, so the result is
equivalent to cos(2*pi*f*n/Fs).
In our case, the sampling frequency Fs = 156.25 kHz, and f is either
125 kHz or 453.125 kHz. Since under sampling is being used, the fre
-
quency of the sampled sinusoid will be different from f. To calculate the
frequency of the resulting sampled sinusoid, the relationship between Fs
and f must be calculated. For f = 125 kHz, ( Fs-f)=(156.25 - 125 ) =
31.25 kHz, so after sampling, a 31.25 kHz sinusoid results. Since
Fs/31.25 = 5, five samples per cycle of the 31.25 kHz result. For f =
453.125 kHz, ( 3*Fs-f)=(468.75 - 453.125 ) = 15.625 kHz. In this case,
Fs/15.625 = 10, so ten samples per cycle of the 15.625 kHz result. In both
cases, coherent sampling is done since an integer number of samples per
cycle is obtained.
THEORY OF OPERATION RECEIVER MODULE
MS462XX MM 2-13