of a SAW i lter. SAW i lters are made on a piezoelectric ceramic substrate such as lithium niobate. A pattern of interdigital i ngers on the surface converts the signals into acoustic waves that travel across the i lter surface. By controlling the shapes, sizes, and spacings of the interdigital i ngers, the response can be tailored to any application. Inter- digital i ngers at the output convert the acoustic waves back to electrical signals.
SAW i lters are normally bandpass i lters used at very high radio frequencies where selectivity is difi cult to obtain. Their common useful range is from 10 MHz to 3 GHz.
They have a low shape factor, giving them exceedingly good selectivity at such high frequencies. They do have a signii cant insertion loss, usually in the 10- to 35-dB range, which must be overcome with an accompanying amplii er. SAW i lters are widely used in modern TV receivers, radar receivers, wireless LANs, and cell phones.
To work over a wide range of frequencies, the integrator RC values must be changed.
Making low and high resistor and capacitor values in IC form is difi cult. However, this problem can be solved by replacing the input resistor with a switched capacitor, as shown in Fig. 2-51(b). The MOSFET switches are driven by a clock generator whose frequency is typically 50 to 100 times the maximum frequency of the ac signal to be i ltered. The resistance of a MOSFET switch when on is usually less than 1000 V. When the switch is off, its resistance is many megohms.
The clock puts out two phases, designated ϕ1 and ϕ2, that drive the MOSFET switches. When S1 is on, S2 is off and vice versa. The switches are of the break- before- make type, which means that one switch opens before the other is closed. When S1 is closed, the charge on the capacitor follows the input signal. Since the clock period and time duration that the switch is on are very short compared to the input signal variation, a brief “sample” of the input voltage remains stored on C1 and S1 turns off.
Now S2 turns on. The charge on capacitor C1 is applied to the summing junction of the op amp. It discharges, causing a current to l ow in the feedback capacitor C2. The resulting output voltage is proportional to the integral of the input. But this time, the gain of the integrator is
f aC1
C2b
where f is the clock frequency. Capacitor C1, which is switched at a clock frequency of f with period T, is equivalent to a resistor value of R5T/C1.
The beauty of this arrangement is that it is not necessary to make resistors on the IC chip. Instead, capacitors and MOSFET switches, which are smaller than resistors, are used. Further, since the gain is a function of the ratio of C1 to C2, the exact capac- itor values are less important than their ratio. It is much easier to control the ratio of matched pairs of capacitors than it is to make precise values of capacitance.
By combining several such switching integrators, it is possible to create low-pass, high-pass, bandpass, and band-reject i lters of the Butterworth, Chebyshev, elliptical, and Bessel type with almost any desired selectivity. The center frequency or cutoff frequency of the i lter is set by the value of the clock frequency. This means that the i lter can be tuned on the l y by varying the clock frequency.
A unique but sometimes undesirable characteristic of an SCF is that the output signal is really a stepped approximation of the input signal. Because of the switching action of the MOSFETs and the charging and discharging of the capacitors, the signal takes on a stepped digital form. The higher the clock frequency compared to the fre- quency of the input signal, the smaller this effect. The signal can be smoothed back into its original state by passing it through a simple RC low-pass i lter whose cutoff frequency is set to just above the maximum signal frequency.
Various SCFs are available in IC form, both dedicated single-purpose or universal versions. Some models can be coni gured as Butterworth, Bessel, Eliptical, or other formats with as many as eight poles. They can be used for i ltering signals up to about 100 kHz. Manufacturers include Linear Technology, Maxim Integrated Products, and Texas Instruments. One of the most popular is the MF10 made by Texas Instruments. It is a universal SCF that can be set for low-pass, high-pass, bandpass, or band-reject operation. It can be used for center or cutoff frequencies up to about 20 kHz. The clock frequency is about 50 to 100 times the operating frequency.
Commutating Filters.
An interesting variation of a switched capacitor i lter is the commutating i lter shown in Fig. 2-52. It is made of discrete resistors and capacitors with MOSFET switches driven by a counter and decoder. The circuit appears to be a low-pass RC i lter, but the switching action makes the circuit function as a bandpass i lter. The operating frequency fout is related to the clock frequency fc and the number N of switches and capacitors used.fc5Nfout and fout5 fc
N
Commutating fi lter
The bandwidth of the circuit is related to the RC values and number of capacitors and switches used as follows:
BW5 1
2πNRC
For the i lter in Fig. 2-52, the bandwidth is BW51y(8πRC).
Very high Q and narrow bandwidth can be obtained, and varying the resistor value makes the bandwidth adjustable.
The operating waveforms in Fig. 2-52 show that each capacitor is switched on and off sequentially so that only one capacitor is connected to the circuit at a time. A sample of the input voltage is stored as a charge on each capacitor as it is connected to the input.
The capacitor voltage is the average of the voltage variation during the time the switch connects the capacitor to the circuit.
Fig. 2-53(a) shows typical input and output waveforms, assuming a sine wave input.
The output is a stepped approximation of the input because of the sampling action of the switched capacitors. The steps are large, but their size can be reduced by simply using a greater number of switches and capacitors. Increasing the number of capacitors from four to eight, as in Fig. 2-53(b), makes the steps smaller, and thus the output more closely approximates the input. The steps can be eliminated or greatly minimized by passing the output through a simple RC low-pass i lter whose cutoff is set to the center frequency value or slightly higher.
One characteristic of the commutating i lter is that it is sensitive to the harmonics of the center frequency for which it is designed. Signals whose frequency is some integer multiple of the center frequency of the i lter are also passed by the i lter, although Figure 2-52 A commutating SCF.
R Input
2- to 4-line decoder
2-bit counter
Bandpass output fout fout ⫽fNc C
S1
S1
S2
S3
S4
2NRC
BW ⫽ 1
S2
C
S3
C
S4
C
T A Clock fc A
Clock
T B B
at a somewhat lower amplitude. The response of the i lter, called a comb response, is shown in Fig. 2-54. If such performance is undesirable, the higher frequencies can be eliminated with a conventional RC or LC low-pass i lter connected to the output.