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Capacitance
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lters like the ones shown here pass the target frequency but also a bunch of others; they work, but don t have a very sharp frequency response. A rst-order lter halves the output signal strength for every doubling of the input frequency away from the cuto frequency. A better lter is the second-order lter which reduces the output strength by 3/4 for every doubling. Third- and fourth-order lters are even more e ective.
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High-pass lter
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A high-pass lter allows high-frequency signals through but reduces the strength of low-frequency signals below the lter s cuto frequency. The cuto frequency is described by equation (10-9). The circuit in Fig. 10-20 is a simple high-pass lter. The input signal at the pad on the left is, optimally, a sine wave for the math to work correctly. Di erent waveforms will behave di erently. We can watch the transformed signal at the test point on the right side of the circuit. An interesting thing to note is that the load that we are driving is the resistor in the RC circuit. If your load has a huge resistance, such that it doesn t really exist in terms of the circuit, you need to add a smaller resistor across it in parallel to provide the R in the RC time constant. The frequency response of this circuit, given a sine input, is: 1 A q 1 f0 =f 2 10-12
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where f0 is the cuto frequency, f is the input frequency, and A is the amplitude gain. Gain is the amount of ampli cation or, in this case, attenuation a circuit provides. Ampli cation increases a signal, with a gain greater than 1. Attenuation decreases a signal, with a gain less than 1. Our high-pass response curve is shown in Fig. 10-21 for an f0 of 1 kHz. Note that the time axis is marked in units of 1 kHz. For low frequencies the output is greatly reduced, while for frequencies above our target of 1 kHz most of the signal gets through.
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Fig. 10-20.
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High-pass RC lter.
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CHAPTER 10 Capacitance
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Fig. 10-21.
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High-pass frequency response.
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Low-pass lter
A low-pass lter is the reverse of a high-pass lter. In this case, we want the lower frequencies to get through while blocking higher frequencies. A simple low-pass lter is shown in Fig. 10-22. If the load is high-impedance, this lter is described by the simple equations listed below. However, be aware that any circuit resistance downstream from the circuit can a ect its behavior. Everything links together. Even though any one piece of a circuit may be simple, all of the pieces working together can be complex and hard to understand. This system complexity is found in any complicated eld of study. We threw in a new word, impedance, which has a symbol Z and is measured in ohms. For a simple DC circuit, impedance is essentially the same as resistance. For AC circuits, it is more complex. In general, impedance is the measure of how a circuit resists, or impedes, current. The frequency response for the circuit in Fig. 10-22 is: 1 A q 1 f=f0 2 This is illustrated in Fig. 10-23 for an f0 of 1 kHz. 10-13
Other lters
There are two other common lters. The band-pass lter is like a low-pass lter followed by a high-pass lter (Fig. 10-24). A band-gap or notch lter
Capacitance
Fig. 10-22.
Low-pass RC lter.
Fig. 10-23.
Low-pass frequency response.
Fig. 10-24.
Band-pass RC lter.
is a little more complicated, allowing frequencies above and below the cuto through but limiting signals at and near the cuto . This is like a high-pass lter in parallel with a low-pass lter (Fig. 10-25). For both of these lters you need to select the high- and low-pass cuto frequencies so that the overlap is correct for the lter shape you want.
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