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Bandpass Filters
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The design of a bandpass filter by image parameters is quite similar to the lowpass and highpass filter design procedure just presented, but the complexity is greater due to twice the components and twice the cutoff frequencies As with the lowpass and highpass filter designs, we also start with a half-section (Fig 639), and can add either of these half-sections together to obtain a filter with more poles With a bandpass filter, each LC pair is a single pole, so a half-section is comprised of two inductors and two capacitors, or two poles Again, as with the above filters, only series arms of each half-section are combined with series arms (or parallel arms to parallel arms), for each half-section (Fig 640); and not with series joined to parallel, or parallel joined to series (Fig 641) To design a bandpass filter with image-parameters, first calculate the element values for the first half-section of Fig 642: RO ( f f ) 2C 1C LS = 2 R ( f f1C ) LP = 2 O 2 C ( f2 C f1C )4 f2 C f1C CS = 2 RO ( f2 C f1C )4 1 R ( f f ) O 2C 1C CP = 2
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L (RO) INPUT
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C (RO) OUTPUT C L (RO) INPUT L
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L (RO) OUTPUT
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FIGURE 639 Series and tank BPF half-sections
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FIGURE 640 Proper way to join BPF half-sections
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FIGURE 641
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Improper way to join BPF half-sections
LS RO
CS RO
FIGURE 642
A BPF half-section
where RO = filter s ZIN and ZOUT f2C = high cutoff frequency f1C = low cutoff frequency Then, combine half-sections to create a filter with more poles as shown in Fig 643 For an example, let us say that a six-pole filter will be required It must have a bandwidth of 50 MHz, located between 475 and 525 MHz, and with a ZIN/ZOUT of 50 First calculate the proper element values for the half-section: 50 (525 MHz 475 MHz) = 159 nH LS = 2 and 525 MHz 475 MHz CS = 2 = 064 pF 50(525 MHz 475 MHz)4
Filter Design
RO LS CS CS LS RO RO LS CS CS LS RO
2 CP
LP /2
a RO CS LS LS CS RO RO CS /2 2 LS RO
FIGURE 643 series
Combining two BPF half-sections when placed (a) tank to tank or (b) series to
and 50(525 MHz 475 MHz) = 159 nH LP = 2 (525 MHz 475 MHz)4 and 1 50 (525 MHz 475 MHz) = 636 pF CP = 2 Transfer these values to Fig 644, the bandpass filter s half-section Begin adding and combining half-sections as shown in Fig 645 Continue combining half-sections until the six-pole filter of Fig 646 is obtained
159 nH LS RO 064 pF CS RO
CP 636 pF
LP 159 nH
FIGURE 644
Values as calculated for BPF half-section
Six
159 nH LS RO 064 pF CS 064 pF CS 159 nH LS RO
CP 636 pF
LP 159 nH
LP 159 nH
CP 636 pF
a 159 nH LS RO 064 pF CS 064 pF CS 159 nH LS RO
2 CP 1272 pF
LP /2 079 nH
FIGURE 645
(a) Two single half-sections, and (b) combining the shunt tanks
159 nH LS RO
064 pF CS
032 pF CS
318 nH LS
032 pF CS
318 nH LS RO
CP 1272 pF
CP LP 079 nH 1272 pF
079 nH 636 pF
LP 159 nH
FIGURE 646
Completed six-pole bandpass lter
Lumped Filter Design Issues
When designing a lumped filter, especially at higher frequencies, the highest Q inductors should be used to lessen insertion losses and the subsequent rounding of the passband edges The capacitors, too, must be chosen carefully, since the filter s characteristics of bandpass, center frequency, and return loss will degrade if these capacitors (or inductors) have a poor tolerance value, deficient high-frequency performance, or inadequate temperature characteristics In fact, the filters as designed may appear fine when a small
Filter Design
production run is tested at room temperature, but may become unacceptable when operated over temperature variations and/or over larger production runs An important specification for filters is their ultimate attenuation characteristics, which strongly depend on the number of filter sections, the unloaded Q of the components (especially the inductors), the parasitic resonances within all the passives, the PCB layout, and any RF shielding employed Lumped (and distributed) filters can become severely detuned if a hand, metallic object, or dielectric material is placed too close to the circuit This is due to the proximity effect, and must be seriously considered when a lumped circuit design is synthesized, simulated, or built (On the average, any RF shield or other conductive structure should be placed at least 200 mils from the top of the largest filter component within the circuit Also, the filter s components, as opposed to the planar layout itself, own reaction to such a metallic structure cannot be readily simulated in any existing RF software) It is normally suggested to utilize odd-order filters in most designs, since evenordered filters can be more vulnerable to termination impedances, possessing a degradation in their frequency responses And many such filters cannot supply a 50- output impedance when specified for even orders, with Chebyshevs being specially problematic in this regard
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