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EXP9: Active Filters
OBJECTIVES
We will investigate the various characteristics of analog passive and active filters. In particular, we will design, analyze, simulate, and observe the following: (i) Low pass, High pass, and Band pass passive RC filters (ii) Low pass, High pass, and Band pass two-pole active filters.
INTRODUCTION^1
Filters are found in various types of electronic equipment and perform various functions. For example, they are used in power supplies to attenuate undesirable ripple, in audio circuits for bass and treble control, and in signal processing applications where they are often used to band limit a signal before it is sampled. There are four basic types of filters: high-pass, low-pass, band-pass and band-reject or notch. All filter implementations fall in one of two categories: passive or active. Passive filters consist of only passive elements, i.e., resistors, inductors and capacitors. On the other hand, active filters consist of passive elements along with active devices, such as transistors or op-amps. It should be noted that one can not take the output of a passive filter and amplify it using an op-amp or transistor to produce an active filter! Typically, op-amps are chosen over transistors in active filters to take advantage of their high performance characteristics and minimal cost.
The question one needs to ask is why bother with active filtering? The answer is really quite simple: an active filter uses combinations of op-amps, resistors and capacitors to obtain a response equal to or better than conventional passive filters. For example, in order to obtain a sharp response with a passive filter, we would need to cascade several passive stages. Each cascaded stage, however, loads the previous stages. This loading attenuates the desired part of the signal, i.e., frequencies within the filter pass-band, as well as unwanted frequency content within signal. This problem is commonly known as insertion loss. Active filtering practically eliminates insertion loss due to the high input impedance and the low output impedance of an op-amp. Furthermore, with active filtering, we can attenuate unwanted frequencies while amplifying desired frequencies! Two other advantages of active filters include simple design and ease of tuning. Lastly, active filters usually do not require the use of inductors, which are typically bulky, costly and depart further from ideal models compared to capacitors.
The Basic Types of Filters There are five basic filter types that bear consideration (shown below in Figure 1): low pass, high pass, band pass, notch, and ìall-passî. Low pass filters (by far the most
(^1) Material in this section were obtained from
http://www.clarkson.edu/class/ee311/Experiment3/Lab3_F02.PDF , http://www.stanford.edu/class/ee122/Handouts/EE122_Labs_02_fall2002.pdf , and Richard Jaeger, Microelectronic Circuit Design, McGraw Hill, 1996.
common type) ideally pass all frequencies below a specific cut-off frequency. High pass filters ideally pass all frequencies above a specific cut-off frequency. Band pass filters ideally have a pass band between a low and a high cut-off frequency and reject frequencies outside of this band. Notch filters ideally reject only a specific, and often very narrow, band of frequencies, passing all others. All-pass filters ideally pass all frequencies equally in amplitude but change the phase of the input signals depending upon their frequency.
Figure 1. Basic Types of Filters
Since some designs in this experiment investigate the performance characteristics of a band-pass filter, we will need to define some important concepts related to band-pass filters. Refer to Figure 2 to obtain some physical intuition to the following terms.
Center Frequency The center frequency, which is sometimes called the resonant frequency, is given by fo. In second order circuits and some higher order circuits, the center frequency is easy to determine since it is the frequency at which the maximum gain of the filter occurs. Theoretically, the center frequency is the geometric mean of the two half-power
frequencies, fL and fH. Therefore, fO = f L ⋅ f H.
Lower and Upper Cutoff Frequencies The lower and upper cutoff (or half-power) frequencies are given by fL and fH , respectively. The lower cutoff frequency is the lower frequency at which the gain is 3dB less than the gain at the center frequency. Similarly, the upper cutoff frequency is the upper frequency at which the gain is 3dB less than the gain at the center frequency.
Maximum Gain The maximum gain of a filter is given by Ho. It is the ratio of Vo to Vi at the filter's center or resonant frequency. Decibels (dB) are often used as a relative measure of filter gain in the lab, where it is common practice to uncalibrate an instrumentation channel so
vout
C
C
R1 R vin
Figure 3. Two-pole Low Pass Active Filter
2 0
(^20)
2 ()^0
Q
s s
AV s (9-1)
where 1 2 1 2
0
RRC C
ω = , ω 0 is the cutoff frequency, and
1 2
1 2 2
1 R R
RR
C
C
Q = ∗ (9-2)
High Pass Active Filters Figure 4
Figure 4. Two-pole High Pass Active Filter
shows a two-pole high pass active filter. The voltage transfer function is specified in equation (9-3).
vout
vin +
C
R
C
R
2 0
(^20)
2 ()
Q
s s
s AV s (9-3)
where 1 2 1 2
0
RRC C
ω = , ω 0 is the cutoff frequency, and
1 2
1 2 1
2 C C
CC
R
R
Q = ∗ (9-4)
Band Pass Active Filters Figure 5
Figure 5. Two-pole Band Pass Active Filter
shows a two-pole band pass active filter. The voltage transfer function is specified in equation (9-5).
vout
R vin
R
C
C
2 0
2 0
0 1 1
( )^22
ω
ω
ω
Q
s s
s RC
RC
AV s (9-5)
where 1 2 1 2
0
RRC C
ω = , ω 0 is the center frequency, and
1 2
1 2 1
2 C C
CC
R
R
Q
PREPARATION
Because the lab assistant does not have all possible values for capacitors, please limit the values you use for the capacitors to those that can be implemented by using few serial and parallel combinations of 0.01μF capacitors.
Low Pass Passive Filter:
- Design a low- pass passive circuit with a single pole that has a cutoff frequency at 20 kHz. Use only capacitors and resistors. For your design, show the values you choose for all passive elements and derive the voltage transfer function.
- For your design, create a PSPICE plot that shows the frequency response for your circuit. Use an AC sweep with a logarithmic X-axis, frequency response from 1 Hz to 100 kHz, and 10 points per decade.
PROCEDURE^2
Low Pass, High Pass, and Band Pass Passive Filters:
- Construct circuits that implement your designs for the passive filters.
- For each of your circuits, measure and plot the voltage gain (Vout/Vin). Also, measure the phase shift from the input to the output. For the measurements, keep Vin at 5Vp-p from function generator, monitor frequency on freq. counter, and measure Vout (p-p) with the oscilloscope. Pay particular attention to the frequency range around cut off. It is important to monitor the input and check/re-adjust to proper 5V p-p at each frequency. Record Vout and the phase shift for each value of the frequency you measure. Plot the frequency response of the voltage gain. Also plot the phase shift as a function of frequency.
Low Pass, High Pass, and Band Pass Active Filters:
- Construct circuits that implement your designs for the active filters.
- For each of your circuits, measure and plot the voltage gain (Vout/Vin). Also, measure the phase shift from the input to the output. For the measurements, keep Vin at 5Vp-p from function generator, monitor frequency on freq. counter, and measure Vout (p-p) with the oscilloscope. Pay particular attention to the frequency range around cut off. It is important to monitor the input and check/re-adjust to proper 5V p-p at each frequency. Record Vout and the phase shift for each value of the frequency you measure. Plot the frequency response of the voltage gain. Also plot the phase shift as a function of frequency.
ANALYSIS
- Compute the cutoff frequencies for all of your circuits, and estimate the rolloff rate for the cutoff frequencies (in dB per decade). In addition, for the Band Pass Filters, compute the Q.
- For each type of filter (low pass, high pass, band pass), compare the performance of the passive and active filters. Explain which of the two technologies you would choose and why.
(^2) Material in this section were obtained from
http://www.educatorscorner.com/experiments/html/exp15.shtml
