Analog-Digital Conversion Handbook: Sampling, Quantisation And Anti-Alias Filter

Sampling Circuit

A digital output will be translated from an analog quantity when the analog input signal is passed through a low pass filter that filters out any high frequency, then samples the analog input signal and finally quantizes the sampled signal. The analog input like the heart beat is converted by a transducer to a Voltage Or Current In A Time domain.(Dan, 1986)

 Sampling allows the acquisition of a stream of instantaneous values that are equally spaced in time and is achieved by the following circuit:

The above circuit comprises of a 741 opamp used as a voltage follower, a MOSFET which gives the sample and hold signal, a capacitor that is a charge storing device and resistors R1 adjusts the offset voltage and R2 is the load resistor. The sampling frequency is;

fs=1/0.04 = 25Hz

the above circuit, the sampled signal is:

he signal to quantisation noise ratio compares a level of signal power versus a level of noise power and it’s the measure of signal strength to background noise.

The quantised signal is

From the sampling theorem, only samples that are less or equal to half the sampling frequency can be accurately covered.(Dan, 1986) The antialiasing circuit filters out all signals above half the sampling rate.

Having R1 as 50Ω, the value of C1 can be calculated from:

: C1=254µF 

The sampling circuit can be improved by increasing the clock amplitude thus reducing the sampling distortion. Oversampling will cause the signal to be sampled at a higher rate than the Nyquist frequency. This creates more samples to be tracked thereby utilizing the dynamic range of the circuit.

When a signal does not remain approximately the same for some consecutive samples it causes the quantization error to appear as a distortion. Dithering improves the digitization of these slowly varying signals by adding a random noise to the analog signal.

The aim of an anti-alias filter is to remove unwanted signals from the input of the analog-to-digital converter or attenuating those signals so as not to adversely affect the signal. This is improved by having a steeper rolloff resulting in a better quality factor achieved using a higher order filter. (Haykin, 1986)

In the the sampling circuit the MOSFET works as a switch. The signal that is to be sampled (Vin) is applied to the drain of MOSFET while the sample and hold control voltage (Vs) is applied to the source of the MOSFET. The source pin of the MOSFET is connected to the non inverting input of the opamp through the resistor R3. During the positive half cycle of the Vs, the MOSFET is ON which acts like a closed switch and the capacitor C1 is charged by the Vin and the same voltage (Vin) appears at the output of the opamp. When Vs is zero MOSFET is switched off and the only discharge path for C1 is through the inverting input of the opamp. Since the input impedance of the opamp is too high the voltage Vin is retained and it appears at the output of the opamp.  

References

Simon Haykin(2001) Communications SystemsJohn Wiley and Sons

Dan Sheingold(1986) Analog-Digital Conversion Handbook,Prentice-

Hall