Methodology for the Digital Calibration of Analog Circuits and Systems: With Case Studies

The most intuitive manner to compensate for imperfections of analog components is to correct their parameters directly. For instance, if the value of a resistor or capacitor influences a time constant which has to be well controlled in a filter [20], it is possible to tune the value of the devices. Another example is the tuning of capacitors in DACs [21].
Figures 26 and 27 present the implementation of digitally adjustable components. By using the switches, it is possible to trim the value of the component. The sub-components can be connected in parallel (figure 26) or in series (figure 27).
The choice of the values of the components in the array can be optimized. Usually, such an array replaces a single component for which the required accuracy cannot be achieved without calibration.
The main issue when designing component arrays is to find the weights of the different elements [22]. In all cases, the layout of the ladder should be done with care in order to match the constituent components and so that the variation between the characteristics of the elements is predicted by equation 2.1.
To keep consistent with the notation used previously and since the unit of the values of the elements in the array can correspond to any physical quantity, depending on the nature of the components (resistors, capacitors, ), the value of component i is named b i.