# Design Note 195: Get 100dB Stopband Attenuation with the LTC1562 Universal Filter Family

The LTC1562 and LTC1562-2 are compact, high performance, "universal"; continuous-time filter products, each containing four 2nd order Operational Filter™ blocks. These low noise, DC-accurate filters let you tailor their center frequencies (f_{0}) over a range of roughly 10kHz to 150kHz (LTC1562) or 20kHz to 300kHz (LTC1562-2) and replace several precision capacitors, resistors and op amps. All frequency-setting components are internal and trimmed, except for one resistor per block, which is desensitized (1% error in this external resistor's value contributes only 0.5% error to the programmed f_{0}). Additional components program each block's Q and gain. A complete application circuit using either the LTC1562 or LTC1562-2 on a surface mount board is about the size of a dime (155mm^{2}).

Figure 1 shows one block, or 2nd order section (each LTC1562 contains four of these), with external resistors to set the standard 2nd order filter parameters f_{0}, Q and gain. In this example, the section is configured so that the two outputs give lowpass and bandpass responses. Cascades of Figure 1 circuits, with appropriate resistor values, can realize any all-pole lowpass or bandpass filter response form such as Chebyshev, Besselor Butterworth. Adding external capacitors permits high pass forms. These filters can suppress undesired frequencies by 100dB while maintaining low noise and distortion.

Operational Filter blocks, however, have many more creative applications. Each block has a flexible virtual-ground input (INV) and two outputs, V1 and V2. V2 is a time integrated version of V1 and therefore lags V1 by 90° over a very wide range of frequencies. Parallel paths into the virtual ground input or from the two different outputs permit transfer-function zeroes, of which one of the most useful is the imaginary-axis zero pair, or notch.

Figure 2 shows a simple and robust notch-filtering method. A notch filter has zero gain at some frequency f_{N}. Notch filters are useful not only to remove frequencies *per se* but also to improve selectivity in lowpass or high pass filters by placing notches in the stopband, as illustrated below. (Such responses are broadly called "elliptics" or "Cauers.")

In Figure 2, a notch occurs when a 2nd order section drives a virtual-ground input through two paths: one through a capacitor and one through a resistor. The virtual ground can be an op amp input, or as in Figure 3, another Operational Filter input. Capacitor C_{N} adds a further 90° to the 90° phase difference between the V1 and V2 voltages. phase difference between the V1 and V2 voltages

At the frequency where currents I_{C} and I_{R} have equal magnitude, the two paths cancel and a 2nd order notch occurs. This frequency is:

f_{N} = √f1 / 2π(R_{N})(C_{N})

Here, f_{1} is a parameter internally trimmed in each Operational Filter product (100kHz in the LTC1562, 200kHz in the LTC1562-2). The notch frequency,

f_{N}, is independent of the center frequencies, f_{0}, programmed separately for each 2nd order section, as in Figure 1.

A remarkable feature of Figure 2 is its inherently deep notch response—the depth does not come from component matching as with other notch-filter circuits. Errors in R_{N} or C_{N} values change the notch frequency, f_{N}, but not the depth of the notch at f_{N}. Moreover, the square root dependence in the f_{N} expression desensitizes the notch frequency to errors in the R_{N} and C_{N} values.

Figure 3 shows an 8-pole modified elliptic response 50kHz lowpass filter using the notch method of Figure 2. In this filter, three operational filter blocks (“B,” “C” and “A” in the pinout, in sequence) drive RC combinations as in Figure 2, giving notches at approximately 133kHz, 167kHz and 222kHz, respectively. A 2nd order lowpass section, per Figure 1 with f_{0} = 55.5kHz, follows (the “D” block in the pinout). Figure 4 shows measured frequency response, which falls 100dB in a little more than one octave. The choice of notch frequencies trades off passband flatness against stopband ripple; the user can explore this tradeoff via analog filter design software such as FilterCAD^{®} for Windows, available free from Analog Devices (1-800-262-5643). The values in Figure 3 give stopband attenuations exceeding 100dB above 140kHz. This circuit has output noise (in 500kHz bandwidth) of 60µV_{RMS} with approximately rail-to-rail input and output swings, or a peak signal-to-noise ratio of 95dB when operating from ±5V supplies. –95dB with 1V_{RMS} (2.8V_{P-P}) output at 20kHz.

Note that 100dB attenuation at hundreds of kilohertz requires electrically clean, compact construction, with good grounding and supply decoupling, and minimal parasitic capacitances in critical paths (such as the INV inputs). For example, 0.1µF capacitors near the LTC1562 provide adequate decoupling from a clean, low inductance power source. But several inches of wire (i.e., a few microhenrys of inductance) from the power supplies, unless decoupled by substantial substantial (≥10µF) capacitance near the chip, can cause a high-Q LC resonance (at hundreds of kHz) in the LTC1562’s supplies or ground reference, impairing SNR and stopband rejection at those frequencies.