This invention relates to electrical filters. More particularly, this invention relates to 2nd order cascadable active-RC filters.
Electrical filters receive signals that typically oscillate between a maximum value and a minimum value (e.g., a sinusoidal signal). These signals are known as AC, or alternating current, signals. (In contrast, signals that maintain a substantially steady value are known as DC, or direct current, signals.) Each oscillation between a maximum and minimum value is a cycle, and the number of cycles per second is the frequency, which is measured in Hertz (one Hertz is one cycle per second). AC signals typically have more than one frequency component. These components can range from low frequencies to high frequencies (e.g., 100 Hz to 100k Hz).
Electrical filters attenuate, or filter out, one or more undesired frequency components from an AC signal, while permitting the other frequency components of the signal to pass through. Depending on the undesired frequencies, different types of filters are used. For example, a low pass filter permits only frequencies below a cutoff frequency to pass through, while frequencies above the cutoff frequency are filtered out. Conversely, a high pass filter permits only frequencies above a cutoff frequency to pass through, while frequencies below the cutoff frequency are filtered out. Band-pass filters permit a range, or band, of frequencies (or only a single frequency) to pass through, while frequencies below a lower bandwidth-edge frequency and above an upper bandwidth-edge frequency are filtered out. Conversely, band-reject or notch filters permit all frequencies except a band of frequencies (or only a single frequency) to pass through. The frequencies allowed to pass through the filter are said to be in the passband, while the filtered out frequencies are said to be in the stopband.
Filters can be of different "orders." For example, filters can be 2nd order low pass filters, 5th order low pass filters, 6th order band-pass filters, and 8th order high pass filters, among many others. The filter order relates mathematically to the transfer function of the filter. The filter transfer function is a ratio of the filter output to the filter input. Typically, this ratio is a function of signal frequency and phase. Filters of the 2nd order are useful because they can be cascaded to form higher order filters. Cascading is the coupling of filters into a series such that the output of one becomes the input of the next.
As is well known in the art, simple circuits including capacitors, inductors, and resistors can be used to construct low pass, highpass, band-pass, and band-reject "passive" filters (e.g., RLC filters). Passive filters provide no signal gain. As such, they are of limited value in many practical applications because signal gain is often required. Furthermore, inductors are generally avoided (particularly at low frequencies) because they have wide tolerances and are bulky, heavy, and non-linear.
"Active" filters provide signal gain and include passive elements and one or more active elements (e.g., transistor devices). Active elements have frequency dependent characteristics and are usually devices that are voltage-dependent or current-dependent. As is known in the art, active filters can be constructed with off-the-shelf operational amplifiers (op amps). However, such op amps usually require numerous external precision components, thus consuming large amounts of circuit board space. Moreover, precision components can be expensive.
Active filters of the 2nd order are characterized by various filter parameters, including center frequency (f.sub.o), quality factor (Q), and filter gain. Cutoff frequencies, mentioned above with respect to low pass and high pass filters, are functions of the center frequency and quality factor. Furthermore, the center frequency, quality factor, and filter gain are functions of the various filter circuit elements, and can be calculated accordingly with known filter equations.
Active filters are typically either available as standard off-the-shelf (usually discrete) circuit devices with fixed filter functions and parameters, or are custom designed as either discrete or integrated circuit devices. In either case, such filters usually cannot be easily modified or adjusted to meet application requirements other than those they were originally designed for. In other words, filter functions and parameters usually cannot be easily modified or adjusted once the filter is manufactured, because doing so usually requires either adding additional components and elements, replacing one or more existing circuit elements with different elements (e.g., replacing a resistor with a capacitor), replacing one or more existing elements with elements of different value (e.g., replacing a 10k ohm resistor with a 150k ohm resistor), or all of the above.
For example, FIG. 1A shows a known 2nd order filter that provides low pass and band-pass frequency responses. Filter 100 includes op amps 103, 113, and 123; resistors 101, 107, 109, 111, 117,and 119; and capacitors 105 and 115. Band-pass response V.sub.1 is available at node 121, while low pass frequency responses V.sub.2 and V.sub.3 are respectively available at nodes 125 and 127. To customize filter 100 to particular filter parameters, values for each of the numerous circuit elements are determined based on a cumbersome series of known design equations.
To subsequently use filter 100 for another application requiring different filter parameters, the circuit element values again need to be determined. This will probably result in one or more of these elements requiring replacement. To replace such elements, sufficient access to and appropriate means of replacing them are required. Such a process is often impractical even if filter 100 is a discrete device, and is more likely impossible if filter 100 is an integrated circuit.
Similarly, modifying filter 100 to perform other filtering functions can be equally difficult. For example, to modify low pass filter 100 to provide 2nd order high pass filtering, the following circuit component and elements should be coupled to filter 100, as shown in FIG. 1B: op amp 153 and resistors 151, 157, 159, and 161. Additional calculations need to be performed to determine the values for resistors 151, 157, 159, and 161, and sufficient space needs to be available to add these parts. High pass frequency response VHP is then available at node 166. However, depending on the specified filter parameters, the values of the other circuit elements of filter 150 may also need to be recalculated. This probably will result in one of more of these elements requiring replacement. Again, this process often is impractical if not impossible.
In sum, users are left with few choices for meeting particular filter applications. For example, users can search for an available off-the-shelf filter; laboriously modify, if possible, an existing filter; or custom design a new filter.
In view of the foregoing, it would be desirable to be able to provide a filter circuit that can be easily configured to provide 2nd order low pass, band-pass, band-reject, and high pass frequency responses.
It would also be desirable to be able to provide a filter circuit that can be easily configured to provide a selectable center frequency, quality factor, and gain.
It would further be desirable to be able to provide a plurality of filter circuits that can be easily configured to construct various types of active filters of 2nd order or higher.
It would still further be desirable to be able to provide a plurality of filter circuits that can be fabricated on a single integrated circuit chip.