Sample and hold
A sample-and - hold circuit (abbreviated to S & H), referred to in English as a sample-and- hold circuit or sample and hold circuit and instantaneous value of scanning is an electronic device which allows analog voltage values for a short time defined at a value to hold. Important parameters are response time, maximum rate of rise and holding drift.
Applications
In the on state, the output voltage of the sample-and- hold circuit to the input voltage follows. When switched off, the sample-and -hold circuit holds the value that had the input voltage at the moment of switching off, as shown in the adjacent figure with zero order. Sample-and- hold circuits with higher order can also supply other values as an instantaneous value. For example, provides a sample-and- hold circuit of the first order to the arithmetic average of the analog input voltage in the measurement interval.
The circuit is generally used in front of an analog-to- digital converter which performs the quantization, but also for synchronous demodulation of signals. In practical analog - to-digital converters, the sample-and- hold circuit is usually integrated, creating a lower price, a smaller footprint and a common specification of both components is ensured.
The use of a sample and hold circuit allows a correct conversion even during rapid changes in input voltage that would without sample and hold circuit lead to incorrect conversion results. Only with itself - compared to the conversion period - very slowly varying stresses may be possible to dispense with the sample and hold circuit.
If the sampling frequency is less than twice the frequency of the measurement voltage, it is called subsampling. The circuit corresponds to a down - mixer high-frequency technology.
In the synchronous demodulator can measure extremely low AC voltage of known frequency, if one only senses the input voltage with a S & H circuit when the voltage to be measured would have reached their maximum value. Interference voltages at other times will be ignored.
A special case is the application of the sample-and- hold approach in liquid crystal displays (LCD). In active matrix displays each picture element (pixel) corresponds to an electric capacitor C1, which is charged to the dynamic image display periodically at each sequential image control according to the desired shade of gray. To during Abtastpause can keep the voltage sufficiently well to each LC pixel, an additional capacitance C2 connected in parallel to the thin film technology, so that a capacity of C = C1 C2 results. The switch S of each capacitance C per pixel is preceded by a thin film field effect transistor. This technique allows the display of video images of high resolution and is therefore used in LCD televisions and computer monitors. Because of Abtastpausen it can in rapid picture Jump to blur come (English motion blur ).
In systems theory, the mathematical transfer function of the sample-and- hold circuit (also holding member zero-order or ZOH element ( zero-order hold) called ) are used for the discretization of continuous-time transfer functions (method see below).
Design and operation
The central element of the sample and hold circuit is a capacitor. He holds in the hold phase, the output voltage at a constant value as possible. In addition, an electronic switch, which determines the sample and hold phase.
The switch is closed, the capacitor is charged through an impedance converter. The impedance converter prevents excessive loading of the voltage source and thus a falsification of the measurement result. In order to get the voltage at the output as long as possible, the capacitor a voltage follower is followed.
According to closing of the switch, the output voltage will not rise immediately to a value of the input voltage, only with a limited slew rate (slew rate). This is determined by the maximum output current of the impedance converter and the size of the capacitor., The voltage on the capacitor has reached the value of the input voltage, a start transient. The duration of the transient is determined primarily by the attenuation of the impedance converter and the resistance of the switch in the closed state. The time which is required until the output voltage swing on the value of the input voltage is within the predetermined tolerance is referred to as time ( acquisition time ).
The switch is open, the capacitor and the voltage follower keeps the output voltage at the value that was present prior to the opening at the entrance.
The time required to switch to the hold state is referred Aperture Time ( Aperture Delay). The Aperture - time varies due to variations in the behavior of the switch. The fluctuations are called Aperture jitter.
Behavior
Due to various disturbing influences the behavior of real sample-and- hold circuits from ideal behavior differs. Here is a short list of effects to be observed.
- Droop or holding drift
- Hold Step
- Feed -through or pass-through
- Parasitic effects of the capacitor
Retainer zero order (image area )
Both in continuous time ( s ), as well as in the discrete-time ( z) image area exist corresponding modeling capabilities of a sample and hold element, which consist of step function and dead-time. An important application of these models is the transfer of a time-continuous (S range) to a time-discrete transfer function ( Z area).
In the Laplace - image area is the transfer function of the holding member zeroth order:
To make the transition to the discrete time domain, is multiplied by a discretization system to function. Thereafter, the z-transform is carried out:
Here, the term corresponding to the continuous time lag element, whose z-transform is ( delay of one sample ).
Thus, the expression to be transformed is simplified to:
Is the discrete-time variant ( h for "hold") of. The resulting function can now be placed in the general shape of an LTI system z- transfer function ( by comparison of coefficients ), which is obtained when discretizing a recursive system structure, thus an IIR system:
The effort in the derivation is very intense in higher-order systems, however, offer program packages in the field of signal processing (MATLAB / Octave) commands to convert. Implementations of the entire procedure are already present. As an example, the transfer function ( 2nd order )
Using the mathematical ZOH element model with a software for this purpose (MATLAB / Octave) are discretized. For this purpose, an indication of the desired sample rate needs to be made, it is set here:
Transfer function = tf ( [2 0], [ 1 0.2 1 ]); c2d (transfer function, 1, ' zoh ') The resulting discrete-time transfer function is:
Where the system output and the system input is. Still, the transfer function is not causal, since they would not have access to previous input values , but on future input values . Therefore, the numerator and denominator is still divided by each, which results in the following transfer function:
A change leads to:
Dissolution of the bracketed expressions:
There is a delay of samples, and the Z transform gives the linear transformation in the discrete time-domain samples for the value of the current:
This procedure made it possible to the transition of a difference equation of an S- transfer function ( which in turn is a differential equation ). This was made possible by the use of a mathematical model of the ZOH member. Applies this method in the digital control technology to produce a transition between analog to digital control loop elements. An alternative method to this is the bilinear transformation.
In the drawing you can see the unit step responses of the two systems. It can be seen that the discrete system function holds the exact value of the continuous function of the system sample time. Even with very large sampling of the exact value of the continuous system is maintained.