While active filters are critical in modern electronics, their design and verification can be tedious and time-consuming. To aid in the design of active filters, Burr Brown offers a range of FilterPro computer-aided design programs using the FILTER42 program. And UAF42 can easily design and implement various active filters UAF42 is a monolithic integrated circuit that contains op amps, matched resistors and precision capacitors required for state variable filter pole pairs Fourth, uncommitted precision op amps also included on the mold.
Filters implemented with UAF42 are time-continuous without the switching noise and aliasing issues of switched capacitor filters Other advantages of the state-variable topology include low sensitivity of filter parameters to external magnitudes and simultaneous low-pass, high-pass, and band-pass A simple two-pole filter for the output can be made with a UAF42 and two external resistors.
A DOS-compatible program guides you through the design process and automatically calculates component values. You can design low-pass, high-pass, band-pass, and band-stop (or notch) filters.
Active filters are designed to approximate the ideal filter response. For example, an ideal low-pass filter eliminates signals above the cutoff frequency (in the stopband), and perfectly passes signals below the cutoff frequency (in the passband) In a practical filter, it is done to approximate the ideal Various tradeoffs. Some filter types are optimized for gain flatness in the passband, some filter types trade off gain variation or ripple in the passband for steeper decay rates between the passband and stopband (in the transition band), and also There are filter types that trade off both flatness and roll-off rate in favor of impulse response fidelity. The FILTER42 supports the three most commonly used all-pole filter types: Butterworth, Chebyshev, and Bessel. The less familiar Inverse Chebyshev is also supported. Select a bipolar bandpass or notch filter and the program defaults to the resonant circuit response.
Butterworth (maximum average). The filter has the flattest passband amplitude response design The attenuation at the cutoff frequency is -3dB The attenuation above the cutoff frequency is a moderately steep -20dB/decade/pole The impulse response of the Butterworth filter has moderate overshoot and oscillation.
Chebyshev (equi-ripple amount) (other transliterated words for Heby]ov in Russian are Tschebychev, Tschebyscheff or Tchevysheff) The initial decay rate of this filter response is much faster than that of Butterworth

Odd-order (5-pole) 3dB ripple Chebyshev low-pass filter response versus frequency, showing cutoff at -3dB.
This advantage comes from the penalty for amplitude variation (ripple) in the passband. Unlike Butterworth and Bessel responses, the Chebyshev cutoff frequency is the frequency at which the response is lower than the ripple band. For even-order filters, all ripples are Above the DC normalized passband gain response, so the cutoff is 0dB For odd order filters, all ripple is below the DC normalized passband gain response, so the cutoff is – (ripple) dB for a given The number of poles allows for a steeper cutoff by allowing more passband ripple. Chebyshev's impulse response is louder than Butterworth, especially in high-ripple designs.
Inverse Chebyshev (equal minimum attenuation in stopband) As the name suggests, this filter type is a close relative of Chebyshev. The difference is that the ripple of an inverse Chebyshev filter is limited to the cutoff band. This filter has a steep roll Fall rate and flat passband amplitude response The cutoff of the inverse Chebyshev is defined as the frequency at which the response first enters the specified stop band, see Figure 3. The step response of the inverse Chebyshev equation is similar to the Butterworth equation.
Bezier (maximum flat time delay), also known as Thomson. Due to its linear phase response, the filter has a good impulse response (minimal overshoot and ringing) for a given number of poles and its magnitude response is not as flat as Butterworth, nor as steep as Butterworth beyond the -3dB cutoff frequency It requires a higher order Bessel filter to give a magnitude response similar to the given Butterworth filter

Response vs frequency for -60dB stop band, inverse Chebyshev low pass filter showing cutoff at -60dB.
Bessel filters can make the added complexity worthwhile.
Tuned Circuit (Resonance or Tuned Circuit Response) If a bipolar bandpass or bandstop (notch) filter is selected, the program defaults to the tuned circuit response. When a bandpass response is selected, the filter design approximates the response of a series LC circuit. When a bipolar bandstop (notch) response is selected, the filter design approximates the response of a parallel LC circuit.
Circuit implementation The filters designed by this program generally use cascaded filter subcircuits to realize the subcircuits either have a bipolar (complex pole pair) response, or have only one real-pole response. The program automatically selects the required subcircuit program according to the function and performance. Options allow you to override the automatic topology selection routine to specify inverted or non-inverted pole pair configurations.
The simplest filter circuit consists of a single-pole pair sub-circuit, as shown in Figure 5, a more complex filter consists of two or more cascaded sub-circuits, and even-order filters are completely implemented by UAF42 pole-pair parts, usually not. Odd-order filters that require external capacitors also require a real-pole section, which can be implemented with a fourth uncommitted op amp in the UAF42, an external resistor, and an external capacitor. This program can be used to design filters up to 10th order.
The program guides you through the filter design and generates component values and a block diagram describing the filter circuit. The filter block diagram program output shows the subcircuits required to implement the filter design labeled by type and connected in the suggested order. The Filter Component Values program The output shows the values of all external components required to implement the filter.

A multistage filter consisting of two or more subcircuits.
The program automatically places the lower Q stage before the higher Q stage to prevent saturation of the op amp output due to gain peaking. Even so, the peaking may limit the input voltage to less than ±10V (VS = ±15V) at The maximum input voltage for each filter design is shown on the filter block diagram. If the UAF42 will operate on a reduced supply, the maximum input voltage must be derated accordingly. To use a filter with a higher input voltage, an input attenuator can be added.
The program designs the simplest filter that provides the required AC transfer function with a passband gain of 1.0V/V. In some cases, the program cannot make a unit main filter and the passband gain will be less than 1.0V/V. In any case, the overall gain of the filter is shown on the filter block diagram. If a different gain is required, additional stages can be added for gain or attenuation as needed.
To build the filter, print out the block diagram and component values Consider one subcircuit at a time. Match the type of subcircuit referenced on the part print to its corresponding circuit diagram. See the Filtering Subcircuits section of this bulletin.
A printed out UAF42 filter component value can show every possible external component needed by any subcircuit Not all of these components require any specific filter design If no value is shown for a component, the component is ignored For example, a complex pole pair The detailed schematic of the subcircuit shows an external capacitor in parallel with the 1000pF capacitor in the UAF42 For filters above about 10Hz, no external capacitor is required.
Once the subcircuits are implemented, connect them in series in the order shown in the filter block diagram.
Filtering subcircuits Filter designs include cascaded complex pole-pair and real-pole subcircuits Complex pole-pair subcircuits are based on UAF42 state variable filter topology This circuit can use six variants, PP1 to PP6 real-pole cross-sections can be used in UAF42 with auxiliary Operational amplifier to achieve. High-pass (HP) and low-pass (LP) real-pole cross-section subcircuits may be referenced by two- or three-letter abbreviations on UAF42 filter component values and filter block diagram program outputs.
The description of each sub-circuit is as follows:
Pole Pair (PP) Subcircuits In general, all complex pole pair subcircuits use the UAF42 pole pair in a state variable configuration. The two filter parameters that must be set are the filter Q and the natural frequency fO. External resistors are used to set these The parameters must be set using two resistors, RF1 and RF2, to set the pole pair fO. A third external resistor, RQ, is usually required to set Q.
At low frequencies, the required value of the frequency setting resistor may be too large. Resistor values higher than about 5MΩ will react with parasitic capacitance, resulting in poor filter performance. When fO is below 10Hz, external capacitors must be added to make the RF1 and RF2 Values remain below 5MΩ when fO is in the range of approximately 10Hz to 32Hz, with internal resistor R2 reducing RF1 and RF2 by √10 and eliminating the need for external capacitors. At the other extreme, when fO is above 10kHz, R2A is connected to R2 is paralleled to improve stability.
External filter gain setting resistor RG is always required when using an inverting pole pair configuration or using a non-inverting configuration with Q<0.57.
Page 1 (Non-vertical pole pair subcircuit using internal gain resistor R3) - In auto topology selection mode, this configuration is used for all bandpass filter responses This configuration allows unity passband gain and high Q (up to 400) A combination of external parts count is minimized since no external gain setting resistors are required.
Page 2 (Non-Vertical Pair Subcircuit Using External Gain Setting Resistors, RG) - Use this configuration when the pole pair Q is less than 0.57.
Page 3 (Reverse Pole Pair Subcircuit) -. In automatic topology selection mode, this configuration is used for all-pole low-pass and high-pass filter responses. This configuration requires an external gain setting resistor RG. When RG=50kΩ, the low-pass and high-pass gains are unified.
Page 4 (Non-Vertical Pole Pair/Zero Subcircuit) - Except for one complex pole pair, this configuration produces a Jω-axis zero (response null) by finding the low-pass and high-pass outputs using auxiliary op-amp A4 in the UAF42 . In automatic topology selection mode, when Q>0.57, this configuration is used for all band-stop (notch) filter responses and inverse Chebyshev filter types. This subcircuit option maintains external components by using internal gain setting resistor R3 low count.
Page 5 (Non-Vertical Pole Pair/Zero Subcircuit) - With the exception of one complex pole pair, this configuration produces a Jω-axis zero (response null) by finding the low-pass and high-pass outputs using auxiliary op-amp A4 in the UAF42 . In automatic topology selection mode, this subcircuit option requires an external gain setting resistor RG when Q<0.57.
(Inverting Pole Pair/Zero Subcircuit) - In addition to one complex pole pair, this configuration produces a Jω-axis zero (response null) by summing the low-pass and high-pass outputs using auxiliary op-amp A4 in the UAF42. This subcircuit is only used when overriding the automatic topology selection algorithm and specifying an inverted pole pair topology and then uses it for all bandstop (notch) filter responses and inverse Chebyshev filter types.

PP1 non-vertical pole pair subcircuit using internal gain setting resistor R3

PP2 non-vertical pole pair subcircuit using external gain setting resistor RG.

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PP6 Inverting pole pair/zero subcircuit.
This subcircuit option requires an external gain setting resistor, RG.
LPs (actual very low-pass subcircuits) Basic low-pass subcircuits (LP). A monopole consists of RP and CP. A2 buffers the output to prevent loading of subsequent stages. If high input impedance is required, an optional buffer A1 can be added at the input.
HP (Real High-Pass Subcircuit) Basic High-Pass Subcircuit (HP). A monopole consists of RP and CP. A2 buffers the output to prevent loading of subsequent stages. If high input impedance is required, an optional buffer A1 can be added at the input.
If not using the auxiliary op amp in the UAF42

If the auxiliary op amp in the UAF42 is not used, connect it as a unity gain follower to ground, as shown in Figure 15. This will keep its inputs and outputs in the linear operating region to prevent bias anomalies that could affect other op amps in the UAF42.
Elimination of LP Subcircuits in Odd-Order Inverse Chebyshev Low-Pass Filters Odd-order inverse Chebyshev low-pass filters can be simplified by eliminating the LP input section and forming real poles in the first pole pair/zero subcircuit in order to The actual poles are formed in the pole pair/zero subcircuit, placing capacitor C1 in parallel with the summing amplifier feedback resistor RZ3 The frequency of the actual pole must be the same as in the low voltage subcircuit One way to achieve this is to set C1=CP and RZ3= RP, where CP and RP are the values specified for the LP section. Then, to keep the gain of the summing amplifier the same, multiply RZ1 and RZ2 by RP/RZ3.
Example of a modified three-pole circuit It is a 347Hz cutoff inverse Chebyshev low pass filter This example is from an application that requires a low pass filter with a notch for 400Hz system power supply noise The cutoff frequency is set A notch standard filter that produces 400Hz for 347Hz consists of two subcircuits, an LP segment followed by a PP4 segment.
In the simplified configuration, the summing amplifier feedback resistor RZ3 was changed from 10kΩ to 130kΩ and in parallel with a 0.01µF capacitor. Note that these values are the same for RP and CP in the LP section. To set the correct summing amplifier gain, resistors RZ1 and RZ2 times RP/RZ3 (130kΩ/10kΩ) RZ1 and RZ2 must be greater than 2kΩ to prevent overloading the op amp output. If necessary, increase RZ1, RZ2, and RZ3 by lowering CP .

Q Enhancement When the fO Q product required for the pole pair cross section is greater than ≈ 100 kHz at frequencies above ≈ 3 kHz, op amp gain and width limitations can cause Q errors and gain peaking. To mitigate this effect, the program is based on a Q compensation algorithm ( 1) Automatic compensation of expected error by reducing design Q When this occurs, the value under the Q heading of the printed UAF42 filter component value will be marked with an asterisk to indicate that it is a theoretical Q, not an actual design Q . The actual design Q will be displayed under the additional heading labeled QCOMP.
Using the FilterPro program, for each data entry, the program automatically calculates the filter performance. This allows you to use a "what if" spreadsheet-type design approach. For example, you can quickly determine the number of poles required for the desired rollover by trial and error.
Getting Started When using the program for the first time, you may need to follow the suggested steps below.
Type to start the program. filter 42
Use the arrow keys to move the cursor to the filter response section.
1) Select Filter Response Press to toggle four response options:
Notch (band stop)
When the desired response appears, move the cursor to the Filter Type section.
2) Select a filter type Move the cursor to the desired filter type and press the selected filter type will be highlighted and marked with an asterisk There are four filter types to choose from:
If Chebyshev is selected, ripple must also be entered (ie, passband ripple see Chebyshev filter description).
If you choose an inverse Chebyshev filter, you must also enter the AMI (that is, the minimum attenuation or maximum gain in the stop band, see Inverse Chebyshev filter description).
3) Enter the filter order Move the cursor to the "Filter order" line in the "Parameters" section and enter the filter order n.
4A) Enter Filter Frequency Move the cursor to the "Filter Frequency" line in the "Parameters" section.
Low Pass/High Pass Filter: Enter f–3dB or cutoff frequency.
Bandpass Filter: Enter the center frequency, fCENTER.
Band Stop (Notch) Filter: Enter the notch frequency fNOTCH.
If your filter is low pass or high pass, go to step 5.
4B) Enter the filter bandwidth If the filter is bandpass or bandstop (notch), move the cursor to the bandwidth line and enter the bandwidth.
If you press on the bandwidth line but don't enter it, you can enter fL and fH instead of the bandwidth fL and fH are the f–3dB points about the center frequency of the Butterworth and Bessel filters they are the ends of the Chebyshev-type ripple band This entry method may force a change in the center frequency or the notch frequency.
5) Print component values Press the function key to print out the filter component values and filter block diagram Assemble the working filter as described in the filter implementation section of this bulletin.
Plotting feature allows you to view graphical results of filter gain and phase versus frequency This feature is useful for comparing filter types.
While viewing the graphical display, you can also use the arrow keys to move the cursor and view the gain and phase of the printed filter response.
Resistor Value The program automatically calculates the resistance value for each entry of data. If an external capacitor is required, the program selects the standard capacitor value and calculates the exact resistance value of the selected filter. The 1% resistance option in the display menu can be used to calculate-
(1) LP Huelsman and PE Allen, "Theory and Design of Active Filters",
Delay to the nearest standard 1% resistor value, not the exact resistor value. To use this feature, move the cursor to the Resistor row in the Filter Response section and press

Capacitor Selection Even-order filters above 10Hz usually do not require external capacitors Odd-order filters require an external capacitor to set the actual pole of the low or high voltage section The choice of capacitor is the key to high performance filters The performance of the capacitors is very different from ideal Large, the introduction of series resistance and inductance limits the size of the Q value, and the nonlinearity of capacitance and voltage will also cause distortion. The 1000pF capacitor in UAF42 is a high-performance type of laser capacitor, and its power is reduced to 0.5%.
If external capacitors are required, the recommended capacitor types are: NPO ceramic, silver mica, metallized polycarbonate; for temperatures up to 85°C, polypropylene or polystyrene are recommended. Common ceramic capacitors with high dielectric constants are avoided. , such as "high-K" type capacitors - they can cause errors in filter circuits.
Op-amp selection In general, you can use the uncommitted fourth op-amp in the UAF42 to implement any necessary LP, HP, or gain stages If you must use additional op-amps, it is important to choose an op-amp that can provide the necessary DC Accuracy, Noise, Distortion and Speed.
Op amp slew rate The op amp's slew rate must be greater than, VOPP, the bandwidth for adequate full power response. For example, an op amp slew rate of at least 6.3V/µs is required to operate at 100kHz, 20Vp-p output. Burr Brown provides an excellent selection of op amps that can be used in the high performance active filter section. The guide above lists some good options.
Op-Amp Bandwidth As a rule of thumb, in both low-pass and band-pass applications, the op-amp bandwidth should be at least 50, GAIN, fO, where GAIN = the noise gain of the op-amp configuration, and fO = filter f–3dB or fCENTER frequency.
In both high-pass and band-stop (notch) applications, the required op amp bandwidth depends on the higher frequencies of interest. As with most active filters, a high-pass filter designed with the UAF42 is converted to a band-pass filter with its The roll-off is determined by the bandwidth of the op amp. The error caused by the roll-off of the op amp can be calculated as follows:
Example of measured UAF42 filter response Actual measured magnitude response plots of 5th order 5kHz Butterworth, 3dB Chebyshev, –60dB inverse Chebyshev, and Bessel lowpass filters designed with this program and implemented with UAF42s. It can be seen that the initial roll-off of the Chebyshev filter is the fastest, and the roll-off of the Bessel filter is the slowest. However, each of the 5th-order all-pole filters ends up rolling at -N, 20dB/decade, where N is the filter order (-100dB/decade for a 5th-order filter).
Oscilloscope photo The step response of each filter is as expected, the Chebyshev filter has the most ringing and the Bessel filter has the least.