Filter Design Introduction

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1 FLORIDA INTERNATIONAL UNIVERSITY Filter Design Introduction Utilizing CAD Tools Christian D. Archilla, B.S.C.E., Research Associate, VLSI Assistant Lab Manager June 2008

2 Table of Contents 1. Introduction Low-Pass and High-Pass Filters Low-Pass Filters High-Pass Filters FilterLab and PSpice FilterLab PSpice Creating Filters Utilizing FilterLab and PSpice Conclusion References

3 1. Introduction A filter is a device that passes electric signals at certain frequencies or frequency ranges while preventing the passage of others. Filter circuits are used in a wide variety of applications. In the field of telecommunication, band-pass filters are used in the audio frequency range (0 khz to 20 khz) for modems and speech processing. High-frequency band-pass filters (several hundred MHz) are used for channel selection in telephone central offices. Data acquisition systems usually require anti-aliasing low-pass filters as well as low-pass noise filters in their preceding signal conditioning stages. System power supplies often use band-rejection filters to suppress the 60-Hz line frequency and high frequency transients. In addition, there are filters that do not filter any frequencies of a complex input signal, but just add a linear phase shift to each frequency component, thus contributing to a constant time delay. These are called all-pass filters. At high frequencies (> 1 MHz), all of these filters usually consist of passive components such as inductors (L), resistors (R), and capacitors (C). They are then called LRC filters. In the lower frequency range (1 Hz to 1 MHz), however, the inductor value becomes very large and the inductor itself gets quite bulky, making economical production difficult. In these cases, active filters become important. Active filters are circuits that use an operational amplifier (op amp) as the active device in combination with some resistors and capacitors to provide an LRC-like filter performance at low frequencies (Figure 1) (Mancini 16-1). Figure 1 Second-Order Passive Low-Pass and Second-Order Active Low-Pass (Mancini 16-1) 2

4 2. Low-Pass and High-Pass Filters 2.1. Low-Pass Filters The following figures introduce the non-inverting and inverting configurations of a firstorder low-pass filter. Figure 2 First-order non-inverting low-pass filter (Mancini 16-12) Figure 3 First-order inverting low-pass filter (Mancini 16-13) After applying the Laplace transformation on low-pass filter circuits, the transfer functions of both configurations yield the following functions: Equation 1 Non-inverting low-pass filter Equation 2 Inverting low-pass filter 3

5 2.2. High-Pass Filters The following figures introduce the non-inverting and inverting configurations of a firstorder high-pass filter. Figure 4 First-order non-inverting high-pass filter (Mancini 16-23) Figure 5 First-order inverting high-pass filter (Mancini 16-23) After applying the Laplace transformation on low-pass filter circuits, the transfer functions of both configurations yield the following functions: Equation 3 Non-inverting high-pass filter Equation 4 Inverting high-pass filter 4

6 3. FilterLab and PSpice 3.1. FilterLab FilterLab is a CAD tool which assists users with the development of active filters. The tool allows the design of low-pass, band-pass, and high-pass filters up to an eighth order filter. In addition, the FilterLab tool allows the use of different responses: Chebychev, Bessel, and Butterworth, ranging from.1 Hz to 10 MHz s. Two different topologies, Sallen Key and Multiple Feedback (MFB), may be utilized PSpice PSpice is a circuit design and simulation CAD tool. PSpice allows for active, passive, analog, and digital schematics to be developed and simulated. PSpice has many different analyses that can be simulated. It contains numerous part libraries which assist in the creation of different types of circuit designs. The creation and simulation of filters yield the magnitude response and the phase response of the individual filters giving the user the ability modify the part values of the filters to create a specific response. 5

7 4. Creating Filters Utilizing FilterLab and PSpice Creating the filters utilizing FilterLab involves several steps. 1. Click on the Design filter button. 2. Choose the filter approximation: Butterworth, Bessel, or Chebychev. 3. Choose the filter type: Low-pass, High-pass, or Band-pass. 4. Type in the overall filter gain in Volta-per-Volts. Figure 6 Setting up a filter using FilterLab 6

8 By default the topology of the low-pass, high-pass, and band-pass filters is Sallen Key. For the low-pass filter the topology could be changed to MFB by clicking on the circuit tab and choosing the MFB topology. Figure 7 FilterLab phase and magnitude response Figure 7 demonstrates the phase and magnitude response plot that is generated by FilterLab. For this filter the corner frequency is 1 KHz and has a phase of -45. From the specified parameter the circuit for the filter is designed using standard components which can be 7

9 easily found. The next step is to construct the filter using PSpice and check the results of both tools.! "# Figure 8 Generated circuit by FilterLab The PSpice circuit is composed of all the components specified by FilterLab. For the operational amplifier (OPAMP), the part number used is ua741. The input to the OPAMP was a VAC with an AC amplitude of 5V and a frequency of 10 KHz. To generate a plot similar to Figure 9 a vphase (found by clicking Markers Mark Advanced) marker is utilized to plot the phase response of the output. The necessary analysis is an AC Sweep analysis, which will 8

10 generate the frequency axis. For the AC Sweep analysis, the Decade AC Sweep Type was utilized. To generate the magnitude response, the output and input of the filter were used along with the following formula. Equation 5 Magnitude in db! "#$! %& Figure 9 Results from PSpice It is evident from Figure 9 and Figure 7 that both results yield the same result. For a deeper analysis of both tools, the order of the filter is changed to an eighth order low-pass filter. 9

11 The simplest way to change the order is by changing the order as in Figure 10. It is apparent the change in the magnitude response of the filter. The corner frequency of the filter remains at 1 KHz however the slope of the filter has increased. The increase of order causes the filter to increase the slope thereby attenuating the undesired frequencies much faster. % $ &' Figure 10 Changing the order of the filter 10

12 The increase in order is also reflected in the circuit of the filter. The filter has 3 additional amplifiers. Each amplifier circuit represents an order two. Figure 11 shows the new amplifiers to the filter. The values of the components change as the order of the filter is either reduced or increased. (# ) Figure 11 Eighth order low-pass filter circuit Utilizing PSpice the circuit is constructed in the same fashion as the first order filter however using the new values. After the circuit is complete the resulting simulation is shown in Figure 12. The results from tools are the same as expected. 11

13 Figure 12 Eighth order PSpice results To demonstrate another type of filter, an eighth order high-pass filter was created using FilterLab and simulated in PSpice. The result of the filter in FilterLab is shown in Figure 13. The corner frequency of the high-pass filter remains at 1 KHz. The undesired frequencies in this case are the low frequencies which are attenuated by the filter. 12

14 &' Figure 13 High-pass filter in FilterLab The results of PSpice, which are shown in Figure 12, correlate with the results from FilterLab. The corner frequency of the PSpice simulation remains at 1 KHz and has the same phase response at the corner frequency as FilterLab. 13

15 &' Figure 14 High-pass filter in PSpice 14

16 5. Conclusion The combination of FilterLab and PSpice to create filters is a powerful mixture. A filter can be designed with FilterLab to have a certain performance and can then be constructed and simulated in PSpice. Of course there are certain limitations in FilterLab. The highest order is an eighth order filter and the approximation type can only be either Chebychev, Butterworth, or Bessel. In addition the frequency only goes up to 10 MHz which limits the number of applications that can use FilterLab. Although there are several limitations, FilterLab and PSpice working together are a great learning tool. The consistency of the results maintained throughout the different constructed filters. In conclusion FilterLab and PSpice could be used to accurately design, create, and simulate any low frequency filter. 15

17 6. References Cadence. 2 June 2008 < Mancini, Ron. "Op Amps For Everyone." Advanced Analog Products. Texas Instruments, August Microchip. 2 June 2008 < 16

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