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Figure 64 T-type constant-K low-pass filter
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Figure 65 Pi-type constant-K low-pass filter
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The point that XL XC is called the resonant frequency (fr), and will vary depending on the values of the LC components The series resonant frequency can be calculated by: fr 1 2 LC
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The formula demonstrates another aspect of resonant circuits: the higher the L and C values, the lower the resonant frequency will be, while the lower the L and C values, the higher the resonant frequency The series bandpass filter will also function as any other series LC circuit would when the input frequency is either above or below this exact point of resonance Since the reactances will now no longer cancel the other, they will create a higher impedance and decrease the current flow A parallel, or resonant, tank circuit will have an impedance that is at a maximum, and current that is at a minimum, at some specific frequency The impedance of the tank will then decrease while the current increases when an input frequency is inserted that is just above or just below this resonance This is the exact opposite effect of that found in the series resonant circuit above However, this resonance point also occurs when XL XC , and is also calculated by: fr 1 2 LC
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The high impedance that is present only at the parallel resonant frequency will attenuate nonresonant frequencies, since only the small chosen band of frequencies will be dropped across the high impedance of the tank Because of the finite Q of components, especially inductors, an inevitable amount of resistance is always present within a tank circuit This will decrease the overall resonant tank impedance which should be infinite and waste power, which must then be replaced The small internal resistance that lowers the tank impedance causes a modest current to flow into the LC
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Downloaded from Digital Engineering Library @ McGraw-Hill (wwwdigitalengineeringlibrarycom) Copyright 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website
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Figure 66 A basic series bandpass filter
Figure 67 A basic series bandstop filter
resonant circuit This waste of power can be minimized by using only high-Q inductors in the tank But because the inductor and capacitor currents in a parallel circuit are 180 degrees out of phase with each other, high circulating currents will always exist within the tank itself during resonance (Fig 68) This circulating current is due to the two LC components exchanging current in a flywheeling manner However, as these currents are completely out of phase, current flow into the tank is always at a minimum, and is dependent on the pure resistance within the tank caused by component Q limitations A simple bandpass filter (BPF) is shown in Fig 69 Since it is an LC parallel filter in shunt with the output, all nonresonant frequencies will be sent to ground, while the bandwidth of interest will be passed on to the output because of the high impedance created by the tank at resonance This creates a selective RF output voltage across the circuit so that it functions as a BPF The bandstop of Fig 610 has the parallel circuit in series with the output Thus, it will pass all frequencies except resonant frequency, which is dropped across the high impedance of the tank Since this will cause a decrease in the output amplitude at this single range of frequencies, it functions as a bandstop filter (BSF) Most filters work by passing any frequencies within the passband with little attenuation while reflecting not absorbing most of the undesired signals within its stopband back toward the source These reflections can become a serious problem in wireless systems design, as we shall soon see Filters must not only shape a signal, reject spurious frequencies, and choose one frequency band out of many, but they must also maintain a specific input and output impedance through much of their passband that is identical to the system s impedance (usually 50 or 75 ohms) Different types of filters, such as LC, crystal, SAW, and distributed, will have various frequency bands in which they are most commonly employed because of size, price, and/or performance: 1 LC filters can be utilized from 1 kHz all the way up to 15 GHz As the frequencies increase, however, so does the difficulty in implementation because of the distributed inductance and capacitance, which conspire to lower the frequency of the filter as designed, as well as distort its response
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