The circuit shown in Figure 1 is a second-order, low-pass filter that falls in the infinite-gain, singlefeedback (IGSF) class. IGSFtype filters are characterized by two-port input and feedback networks.
Some common two-ports typically used in filters are the tee network and its bridged-tee and twin-tee derivatives. If a digitally controlled potentiometer and a capacitor are used to implement the tee network, variability and programmability are added to the circuit.
The IGSF filter shown in the figure is basically an inverting amplifier in which the input circuit A is a tee network and the feedback circuit B is a bridged-tee network.
The movement of the potentiometer wiper introduces a new degree of freedom k to the filter design. Here, k is a number that varies from 0 to 1 and reflects the proportionate position of the wiper from one end of the potentiometer (k = 0) to the other end (k = 1).
The gain expression or transfer function of the filter is determined by finding the ratio of the short-circuit admittance coefficients of the input and feedback networks. For this circuit, VO/VS is defined by Equation 1 (Equation Listing).
The classic expression for a second-order filter is given by Equation 2 (see “Equation Listing,” p. 102). In this equation, AO, ωO, and Q represent the passband gain, characteristic frequency, and figure of merit, respectively.
From the gain expression:
The movement of the wiper, described by k(1 − k) in the expressions for ωO and Q, is parabolic. Depending on the application, the digitally controlled potentiometers can be programmed to optimize the characteristic frequency ωO or the quality factor Q of the filter. The accuracy of the filter parameters depends on the component sensitivities and the tolerances of the component values.
Obtaining precise values for the parameters is difficult to achieve because precision capacitors are expensive and in limited supply. Such a limitation in performance can be overcome using the programmable tee network. The X9418 is a dual potentiometer device with 2-wire (I2C) interface, which the ganging of the potentiometer wipers achieved via software.
For the circuit values shown in Figure 1, the filter can be programmed for theoretical maximally flat magnitude (MFM or Butterworth) response when k = 13/63. For this value of k, Q 0.704 and fC = 6.85 kHz. The measured response for this setting is shown in Figure 2. When the programmable tee network is at its limit (k = 0 or k = 1), the circuit reduces to a first-order low-pass RC filter whose cutoff frequency is determined by the 10k resistance of the potentiometer and the value of C2.
The inclusion of an electronic potentiometer adds variability to this filter circuit and new capabilities to its associated digital controls. Through its computer-controlled serial bus, it provides programmability.
An automated closed-loop calibration procedure to program or calibrate the filter can be implemented to save test time and provide enhanced performance and security.