DECLARATION

This is to certify that Thesis/Report entitled “MICROWAVE BAND PASS FILTER”which is submitted by us in particalfulfillment of the requirement for the award of degree B.Tech. in Electronics and communication Engineering to G. B. pant Engineering College comprises only our original work and guidance of our guide

Date: Name of Students Rahul Kumar(05320902810),Sanjay singh(07020902810),

Manish Bansal(08120902810),KuldeepAhirwar(07520902810)

APPROVED BY

HOD(ECE)

G. B. Pant Engineering College

Certificate

This is to certify that Project entitled “MICROWAVE BAND PASS FLTER”submitted in partial fulfillment of the requirement of the award of degree B.Tech. in Electronics & Communication Engineering at G.B. Pant Engineering College is an authentic work carried out by them under my guidance. I wish all success for their future endeavours.

Mrs. Mamata jain Mr. Krishna ranshu ranjan

(HOD ECE) (Assistant professor ECE)

2

Microwave Band pass flter

Minor Project Report submitted in partial fulfillment of the requirement for the degree of

B.Tech.In

Electronics and communication Engineering

ByRahul Kumar(05320902810)Sanjay Singh(07020902810)

Manish Bansal(08120902810)KuldeepAhirwar(07520902810)

Under the Guidance ofMr .Krishna RanshuRanjan

(Assistant Professor ,ECE)

ToDepartment of Electronics and Communication

Engineering G. B. Pant Engineering College

(Govt. of NCT of Delhi)OKHLA INDUSTRIAL ESTATE,PHASE-3NEW DELHI-110020

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Filter Types

There are four types of filter :-

Low pass

High pass

Band pass

Band stop

LOW PASS FILTER :- The low pass filter allows low frequency signal to be transmitted

from the input to the output port with little attenuation .However , as the frequency exceeds a

certain cutoff point , the attenuation increase significantly with the result of delivering an

amplitude reduced signal to the output .

HIGH PASS FILTER :-The high pass filter passes the high frequency signal which is above

the cutoff point & attenuates low frequency which is below the cutoff point.

BAND PASS FILTER :- The filter that passes the band of frequencies & attenuates all other

frequencies which is not coming in this band .

BAND STOP FILTER :-The filter that attenuate a band of frequencies that attenuate a band

of frequencies & passes the remaining frequencies with little attenuation .

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ButterWorth Low pass Filter :-It is also called binomial filter .

It exhibits a monotonic attenuation profile. But it has a disadvantage that to achive a steep attenuation trasition from pass band to

stop band , a large number of component is needed . To remove this disadvantage chebyshev filter is introduced.

ChebyshevFilter :-This filter has ripple either in passband or stopband for a steeper transition.

Elliptic Filter:- This filter has ripple in both bands , passband as well as stopband .This filter has steepest transition.

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Parameters

In analysing the various trade off when dealing with filters , the following parameters play key role :-

insertion loss Ripple Bandwidth Shape factor Quality factor

Insertion loss :- An ideal filter when inserted into the RF ckt. path would introduce no power loss in the pass band i.e. insertion loss is zero But practical filter introduce some power loss . so, the insertion loss quantifies how much below the 0dB line the power amplitude response drops .

In mathematically , assuming the filter to a source with zs=zo.

IL=10 log(PA/PL) =-20log|S21|

where PA =Available power from source

PL=Power delivered to the load

S21=Filter S parameter ,Characterising signal transmission power from ports to ports .

Ripple :-The flatness of the signal in the pass band can be quantified by specifying the ripple o difference between max. and min. amplitude response in either dB or nepers.

Bandwidth :- For a band pass filter ,bandwidth defines the difference between upper and lower frequency ,Typically recorded at the points of 3dB attenuation above the passband .

BW=fu3dB – fl

3dB

Shape Factor :-This factor describes the sharpness of the response by taking the ratio between the 60 dB & 3B bandwidths

SF=BW60dB/BW3dB =fu60dB – fl

60dB /fu3dB – fl

3dB

Quality Factor :-

This factor describes the selectivity of the filter . It is defined as the ratio of the average stored energy to the energy loss per cycle at the resonant frequency .

Q =2π average energy stored /energy loss per cycle ῳ=ῳc

In applying this definition , care must be taken to distinguish between an loaded and unloaded filter .

When the power loss consists of power loss associated with external load and the filter .the resulting quality factor is named loaded Q or QLD. then,

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1/QLD=1/ῳ(Power loss in filter /average stored energy )ῳ=ῳc

1/QLD=1/QF + 1/QE

where QF= Filter Q

QE=External Q

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Low Pass FilterBy definition, a low-pass filter is a circuit offering easy passage to low-frequency signals and difficult passage to high-frequency signals. There are two basic kinds of circuits capable of accomplishing this objective, and many variations of each one: The inductive low-pass filter in Figure below and the capacitive low-pass filter in Figure below

Inductive low-pass filter

The inductor's impedance increases with increasing frequency. This high impedance in series tends to block high-frequency signals from getting to the load.

The response of an inductive low-pass filter falls off with increasing frequency.

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Capacitive low-pass filter.The capacitor's impedance decreases with increasing frequency. This low impedance in parallel with the load resistance tends to short out high-frequency signals, dropping most of the voltage across series resistor R1.

The response of a capacitive low-pass filter falls off with increasing frequency.

The inductive low-pass filter is the pinnacle of simplicity, with only one component comprising the filter. The capacitive version of this filter is not that much more complex, with only a resistor and capacitor needed for operation. However, despite their increased complexity, capacitive filter designs are generally preferred over inductive because capacitors tend to be “purer” reactive components than inductors and therefore are more predictable in their behavior. By “pure” mean that capacitors exhibit little resistive effects than inductors, making them almost 100% reactive. Inductors, on the other hand, typically exhibit significant dissipative (resistor-like) effects, both in the long lengths of wire used to make them, and in the magnetic losses of the core material. Capacitors also tend to participate less in “coupling” effects with other components (generate and/or receive interference from other components via mutual electric or magnetic fields) than inductors, and are less expensive.

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However, the inductive low-pass filter is often preferred in AC-DC power supplies to filter out the AC “ripple” waveform created when AC is converted (rectified) into DC, passing only the pure DC component. The primary reason for this is the requirement of low filter resistance for the output of such a power supply. A capacitive low-pass filter requires an extra resistance in series with the source, whereas the inductive low-pass filter does not. In the design of a high-current circuit like a DC power supply where additional series resistance is undesirable, the inductive low-pass filter is the better design choice. On the other hand, if low weight and compact size are higher priorities than low internal supply resistance in a power supply design, the capacitive low-pass filter might make more sense.

All low-pass filters are rated at a certain cutoff frequency. That is, the frequency above which the output voltage falls below 70.7% of the input voltage. This cutoff percentage of 70.7 is not really arbitrary, all though it may seem so at first glance. In a simple capacitive/resistive low-pass filter, it is the frequency at which capacitive reactance in ohms equals resistance in ohms. In a simple capacitive low-pass filter (one resistor, one capacitor), the cutoff frequency is given as:

Inserting the values of R and C from the last SPICE simulation into this formula, we arrive at a cutoff frequency of 45.473 Hz. However, when we look at the plot generated by the SPICE simulation, we see the load voltage well below 70.7% of the source voltage (1 volt) even at a frequency as low as 30 Hz, below the calculated cutoff point. What's wrong? The problem here is that the load resistance of 1 kΩ affects the frequency response of the filter, skewing it down from what the formula told us it would be.

High pass Fillter

High-pass filter's task is just the opposite of a low-pass filter: to offer easy passage of a high-frequency signal and difficult passage to a low-frequency signal. As one might expect, the inductive and capacitive versions of the high-pass filter are just the opposite of their respective low-pass filter designs.

Capacitive high-pass filter.The capacitor's impedance (Figure above) increases with decreasing frequency. (Figure below) This high impedance in series tends to block low-frequency signals from getting to load.

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The response of the capacitive high-pass filter increases with frequency.

Inductive high-pass filter.The inductor's impedance (Figure above) decreases with decreasing frequency. (Figure below) This low impedance in parallel tends to short out low-frequency signals from getting to the load resistor. As a consequence, most of the voltage gets dropped across series resistor R1.

The response of the inductive high-pass filter increases with frequency.

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This time, the capacitive design is the simplest, requiring only one component above and

beyond the load. And, again, the reactive purity of capacitors over inductors tends to favor

their use in filter design, especially with high-pass filters where high frequencies commonly

cause inductors to behave strangely due to the skin effect and electromagnetic core losses.

As with low-pass filters, high-pass filters have a rated cutoff frequency, above which the

output voltage increases above 70.7% of the input voltage. Just as in the case of the capacitive

low-pass filter circuit, the capacitive high-pass filter's cutoff frequency can be found with the

same formula:

In the example circuit, there is no resistance other than the load resistor, so that is the value

for R in the formula.

Periodic Structure

An infinite transmission line or waveguide periodically loaded with reactive elements is

an example of a periodic structure. As shown in Figure 8.1, periodic structures can take

various forms, depending on the transmission line media being used. Often the loading

elements are formed as discontinuities in the line itself, but in any case they can be modeled

as lumped reactances in shunt (or series) on a transmission line, as shown in Figure 8.2.

Periodic structures support slow-wave propagation (slower than the phase velocity of

theunloaded line), and have passband and stopband characteristics similar to those of filters;

they find application in traveling-wave tubes, masers, phase shifters, and antennas.

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Analysis of Infinite Periodic Structures

We first consider the propagation characteristics of the infinite loaded line shown in Figure

8.2. Each unit cell of this line consists of a length, d, of transmission line with a shunt

susceptance across the midpoint of the line; the susceptance, b, is normalized to the

characteristic

impedance, Z0. If we consider the infinite line as being composed of a cascade

of identical two-port networks, we can relate the voltages and currents on either side of the

nth unit cell using the ABCD matrix.

whereA, B,C, and D are the matrix parameters for a cascade of a transmission line section

of length d/2, a shunt susceptanceb, and another transmission line section of length d/2.

From Table 4.1 we then have, in normalized form,

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whereθ = kd, and k is the propagation constant of the unloaded line. The reader can verify

thatAD − BC = 1, as required for reciprocal networks.

For a wave propagating in the +z direction, we must have

V(z) = V(0)e−γ z , (8.3a)

I (z) = I (0)e−γ z , (8.3b)

for a phase reference at z = 0. Since the structure is infinitely long, the voltage and current

at the nth terminals can differ from the voltage and current at the n + 1 terminals only by

the propagation factor, e−γ d . Thus,

Vn+1 = Vne−γ d ,(8.4a)

In+1 = Ine−γ d .(8.4b)

Using this result in (8.1) gives the following:

For a nontrivial solution, the determinant of the above matrix must vanish:

AD + e2γ d −(A + D)eγd −BC = 0, (8.6)

or, since AD −BC = 1,

1 + e2γ d −(A + D)eγd = 0,

e−γd + eγd = A + D,

coshγ d = A + D/2

= cosθ –b/2

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sinθ, (8.7)

where (8.2) was used for the values of A and D. Now, if γ = α + jβ, we have that

coshγ d = cosh αd cosβd + j sinhαd sin βd = cosθ –b/2

sinθ. (8.8)

Since the right-hand side of (8.8) is purely real, we must have either α = 0 or β = 0.

Case 1: α = 0, β _= 0. This case corresponds to a nonattenuated propagating wave on the

periodic structure, and defines the passband of the structure. Equation (8.8) reduces to

cosβd = cosθ –b/2

sinθ, (8.9a)

which can be solved for β if the magnitude of the right-hand side is less than or equal to

unity. Note that there are an infinite number of values of β that can satisfy (8.9a).

Case 2: α _= 0, β = 0, π. In this case the wave does not propagate, but is attenuated along

the line; this defines the stopband of the structure. Because the line is lossless, power is not

dissipated, but is reflected back to the input of the line. The magnitude of (8.8) reduces to

which has only one solution (α >0) for positively traveling waves;α <0 applies for

negatively

traveling waves. If cosθ −(b/2) sin θ ≤−1, (8.9b) is obtained from (8.8) by letting

β = π; then all the lumped loads on the line are λ/2 apart, yielding an input impedance

the same as if β = 0.

Thus, depending on the frequency and normalized susceptance values, the periodically

loaded line will exhibit eitherpassbands or stopbands, and so can be considered as a type

of filter. It is important to note that the voltage and current waves defined in (8.3) and (8.4)

are meaningful only when measured at the terminals of the unit cells, and do not apply to

voltages and currents that may exist at points within a unit cell. These waves are similar to

the elastic waves (Bloch waves) that propagate through periodic crystal lattices.

Besides the propagation constant of the waves on the periodically loaded line, we

will also be interested in the characteristic impedance for these waves. We can define a

characteristic impedance at the unit cell terminals as

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The ± solutions correspond to the characteristic impedance for positively and negatively

traveling waves, respectively. For symmetric networks these impedances are the same except

for the sign; the characteristic impedance for a negatively traveling wave is negative

because we have defined In in Figure 8.2 as always being in the positive direction.

From (8.2) we see that B is always purely imaginary. If α = 0, β _= 0 (passband), then

(8.7) shows that cosh γ d = A ≤ 1 (for symmetric networks), and (8.12) shows that ZB will

be real. If α _= 0, β = 0 (stopband), then (8.7) shows that cosh γ d = A ≥ 1, and (8.12)

shows that ZB is imaginary. This situation is similar to that for the wave impedance of a

waveguide, which is real for propagating modes and imaginary for cutoff, or evanescent,

modes.

Terminated Periodic Structures

Next consider a truncated periodic structure terminated in a load impedance ZL, as shown

in Figure 8.3. At the terminals of an arbitrary unit cell, the incident and reflected voltages

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and currents can be written as (assuming operation in the passband)

Vn= V+0e−jβnd+ -0e jβnd(8.13a)

In = I+0e−jβnd+ I0

-e jβnd=V0+/Z+Be−jβnd+V0

-/Z-Be jβnd(8.13b)

where we have replaced γ z in (8.3) with jβndsince we are interested only in terminal

quantities.

Now define the following incident and reflected voltages at the nth unit cell:

In order to avoid reflections on the terminated periodic structure we must have ZL =

ZB, which is real for a lossless structure operating in a passband. If necessary, a quarterwave

transformer can be used between the periodically loaded line and the load.

k -β Diagrams and Wave Velocities

When studying the passband and stopband characteristics of a periodic structure, it is useful

to plot the propagation constant, β, versus the propagation constant of the unloaded line,

k(or ω). Such a graph is called a k-β diagram, or Brillouindiagram, after L. Brillouin, a

physicist who studied wave propagation in periodic crystal structures.

The k-β diagram can be plotted from (8.9a), which is the dispersion relation for a

general periodic structure. In fact, a k-β diagram can be used to study the dispersion

characteristics

of many types of microwave components and transmission lines. For instance,

consider the dispersion relation for a waveguide mode:

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wherekcis the cutoff wave number of the mode, k is the free-space wave number, and β

is the propagation constant of the mode. Relation (8.19) is plotted in the k-β diagram of

Figure 8.4. For values of k <kcthere is no real solution for β, so the mode is nonpropagating.

For k >kcthe mode propagates, and k approaches β for large values of β (TEM

propagation).

The k-β diagram is also useful for interpreting the various wave velocities associated

with a dispersive structure. The phase velocity is

vp= ω/β= ck/β , (8.20)

which is seen to be equal to c (speed of light) times the slope of the line from the origin to

the operating point on the k-β diagram. The group velocity is

vg= dω/dβ= cdk/dβ , (8.21)

which is the slope of the k-β curve at the operating point. Thus, referring to Figure 8.4,

we see that the phase velocity for a propagating waveguide mode is infinite at cutoff and

approachesc (from above) as kincreases. The group velocity, however, is zero at cutoff and

approachesc (from below) as kincreases. We finish our discussion of periodic structures

with a practical example of a capacitively loaded line.

FILTER DESIGN BY THE IMAGE PARAMETER METHOD

The image parameter method of filter design involves the specification of passband and

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stopband characteristics for a cascade of simple two-port networks, and so is related in

concept

to the periodic structures of Section 8.1. The method is relatively simple but has the

disadvantage that an arbitrary frequency response cannot be incorporated into the design.

This is in contrast to the insertion loss method, which is the subject of the following section.

Nevertheless, the image parameter method is useful for simple filters, and it provides a link

between infinite periodic structures and practical filter design. The image parameter method

also finds application in solid-state traveling-wave amplifier design.

Image Impedances and Transfer Functions for Two-Port Networks

We begin with definitions of the image impedances and voltage transfer function for an

arbitrary reciprocal two-port network; these results are required for the analysis and design

of filters by the image parameter method.

Consider the arbitrary two-port network shown in Figure 8.7, where the network is

specified by its ABCD parameters. Note that the reference direction for the current at port 2

has been chosen according to the convention for ABCD parameters. The image impedances,

Zi1 and Zi2, are defined for this network as follows:

Zi1 = input impedance at port 1 when port 2 is terminated with Zi2

Zi2 = input impedance at port 2 when port 1 is terminated with Zi1.

Thus both ports are matched when terminated in their image impedances. We can derive

expressions for the image impedances in terms of the ABCD parameters of the network.

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Two important types of two-port networks are the T and π circuits, which can be

made in symmetric form. Table 8.1 lists the image impedances and propagation factors,

along with other useful parameters, for these two networks.

Constant-k Filter Sections

We can now develop low-pass and high-pass filter sections. First consider the T-network

shown in Figure 8.9. Intuitively, we can see that this is a low-pass filter network because

the series inductors and shunt capacitor tend to block high-frequency signals while passing

low-frequency signals. Comparing with the results given in Table 8.1, we have Z1 = jωL

andZ2 = 1/jωC, so the image impedance is

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and a nominal characteristic impedance, R0, as

2. Forω>ωc: This is the stopband of the filter section. Equation (8.35) shows that ZiT

is imaginary, and (8.36) shows that eγis real and −1 <eγ<0 (as seen from the

limits as ω → ωcand ω→∞). The attenuation rate for ω ωcis 40 dB/decade.

Typical phase and attenuation constants are sketched in Figure 8.10. Observe that the

attenuation, α, is zero or relatively small near the cutoff frequency, although

α→∞asω→∞.This type of filter is known as a constant-k low-pass prototype. There are only

two parameters to choose (L and C), which are determined by ωc, the cutoff frequency,

andR0, the image impedance at zero frequency.

The above results are valid only when the filter section is terminated in its image

impedance at both ports. This is a major weakness of the design because the image impedance

is a function of frequency, and is not likely to match a given source or load impedance.

This disadvantage, as well as the fact that the attenuation is rather low near cutoff, can be

remedied with the modified m-derived sections to be discussed shortly.

For the low-pass π-network of Figure 8.9, we have that Z1 = jωLand Z2 = 1/jωC,

so the propagation factor is the same as that for the low-pass T-network. The cutoff

frequency,

ωc, and nominal characteristic impedance, R0, are the same as the corresponding

quantities for the T-network as given in (8.33) and (8.34). At ω = 0 we have that

ZiT= Ziπ = R0, where Ziπ is the image impedance of the low-pass π-network, but ZiT

andZiπ are generally not equal at other frequencies.

High-pass constant-k sections are shown in Figure 8.11; we see that the positions of

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the inductors and capacitors are reversed from those in the low-pass prototype. The design

equations are easily shown to be

m-Derived Filter Sections

We have seen that the constant-k filter section suffers from the disadvantages of a relatively

slow attenuation rate past cutoff, and a nonconstant image impedance. The m-derived filter

section is a modification of the constant-k section designed to overcome these problems. As

shown in Figure 8.12a, b the impedances Z1 and Z2 in a constant-k T-section are replaced

withZ1 and Z2, and we let

Z1’=mZ1 .

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If we restrict 0 < m <1, then these results show that eγis real and |eγ| >1 for ω >ωc.

Thus the stopband begins at ω = ωc, as for the constant-k section. However, when ω =

ω∞, where

ω∞ =ωc/ √ 1 − m2

the denominators vanish and eγbecomes infinite, implying infinite attenuation. Physically,

this pole in the attenuation characteristic is caused by the resonance of the series LC resonator

in the shunt arm of the T; this is easily verified by showing that the resonant frequency

of this LC resonator is ω∞. Note that (8.44) indicates that ω∞ >ωc, so infinite

attenuation occurs after the cutoff frequency, ωc, as illustrated in Figure 8.14. The position

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of the pole at ω∞ can be controlled with the value of m.

We now have a very sharp cutoff response, but one problem with the m-derived section

is that its attenuation decreases for ω > ω∞. Since it is often desirable to have infinite

attenuation as ω→∞, the m-derived section can be cascaded with a constant-k section to

give the composite attenuation response shown in Figure 8.14.

The m-derived T-section was designed so that its image impedance was identical to

that of the constant-k section (independent of m), so we still have the problem of a

nonconstant

image impedance. However, the image impedance of the π-equivalent will depend

onm, and this extra degree of freedom can be used to design an optimum matching section.

The easiest way to obtain the corresponding π-section is to consider it as a piece

of an infinite cascade of m-derived T-sections, as shown in Figure 8.15. Then the image

impedance of this network is, using the results of Table 8.1 and (8.35),

Since this impedance is a function of m, we can choose m to minimize the variation of Ziπ

over the passband of the filter. Figure 8.16 shows this variation with frequency for several

values of m; a value of m = 0.6 generally gives the best results.

This type of m-derived section can then be used at the input and output of the filter to

provide a nearly constant impedance match to and from R0. However, the image impedance

of the constant-k and m-derived T-sections, ZiT, does not match Ziπ; this problem can be

surmounted by bisecting the π-sections, as shown in Figure 8.17. The image impedances

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of this circuit are Zi1 = ZiTand Zi2 = Ziπ , which can be shown by finding its ABCD

parameters:

Composite FiltersBy combining in cascade the constant-k, m-derived sharp cutoff and the m-derived matching

sections we can realize a filter with the desired attenuation and matching properties.

This type of design is called a composite filter, and is shown in Figure 8.18. The sharpcutoffsection, with m <0.6, places an attenuation pole near the cutoff frequency to providea sharp attenuation response; the constant-k section provides high attenuation further intothestopband. The bisected-π sections at the ends of the filter match the nominal source

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and load impedance, R0, to the internal image impedances, ZiT, of the constant-k andm-derived sections. Table 8.2 summarizes the design equations for low- and high-passcomposite filters; notice that once the cutoff frequency and impedance are specified, thereis only one degree of freedom (the value of m for the sharp-cutoff section) left to controlthe filter response. The following example illustrates the design procedure.

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Filter Transformation :-

Lowpass to highpass

The frequency transformation required in this case is:

where ωc is the point on the highpass filter corresponding to ωc' on the prototype. The transfer

function then transforms as:

Inductors are transformed into capacitors according to,

and capacitors are transformed into inductors,

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the primed quantities being the component value in the prototype.

Lowpass to bandpass

In this case, the required frequency transformation is:

where Q is the Q-factor and is equal to the inverse of the fractional bandwidth:

If ω1 and ω2 are the lower and upper frequency points (respectively) of the bandpass response

corresponding to ωc' of the prototype, then,

and

Δω is the absolute bandwidth, and ω0 is the resonant frequency of the resonators in the filter.

Note that frequency scaling the prototype prior to lowpass to bandpass transformation does

not affect the resonant frequency, but instead affects the final bandwidth of the filter.

The transfer function of the filter is transformed according to:

The prototype filter above, transformed to a 50Ω, 6MHz bandpass filter with 100kHz

bandwidth

Inductors are transformed into series resonators,

and capacitors are transformed into parallel resonators,

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Example 1

AIM: - Design a hi-lo impedance low pass filter having a maximally flat response and a cut off frequency of 2.5 GHz. It is necessary to have more than 10 dB insertion loss at 4 GHz. The filter impedance is 50 Ω; the highest practical line impedance is 120 Ω, and the lowest is 20 Ω. Consider the effect of losses when this filter is implemented with a microstrip substrate having h=0.158 cm, €r=4.2, tan δ=0.02, and copper conductor of 0.5 mil thickness.

DESIGN STEPS:-

Series inductor can be replaced by high impedance line. Shunt capacitor can be replaced by low impedance line.

CALCULATION :-

For fc=2.5 GHz and above 10 dB insertion loss at 4 GHz the filter will be a 3rd order filter.

electrical length is given by

βl=LZ0/Zh ................... for inductor

βl=CZl/Z0 ................... for capacitor

where L and C are normalised element values and Z0 is filter impedance.

Zh= 120 Ω; Zl= 20 Ω

For a 3rd order filter;

g1= 1.0=L1, g2=2.0=C2, g3=1.0=L3

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The required electrical length, physical microstrip line width, and length are given below:-

Section Z(Ω) βl (degree) W (mm) l (mm)

1 120 23.87 0.417 4.675

2 20 45.8 11.591 7.863

3 120 23.87 0.417 4.675

TLINE SCHEMATIC:-

After analyzing the circuit, S-parameters on a rectangular plot are as follow:

TLINE PLOT:-

32

MLINE PLOT:-

33

SONNET PPLOT:-

34

Example 2

AIM: - Design a hi-lo impedance low pass filter having a maximally flat response and a cut off frequency of 2.5 GHz. It is necessary to have 20 dB insertion loss at 4 GHz. The filter impedance is 50 Ω; the highest practical line impedance is 120 Ω, and the lowest is 20 Ω. Consider the effect of losses when this filter is implemented with a microstrip substrate having h=0.158 cm, €r=4.2, tan δ=0.02, and copper conductor of 0.5 mil thickness.

For fc=2.5 GHz and above 10 dB insertion loss at 4 GHz the filter will be a 5th order filter.

For a 5th order filter;

g1=0.6180=g5, g2=1.6180=g4, g3==2.000

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The required electrical length, physical microstrip line width, and length are given below:-

Section Z(Ω) βl (degree) W (mm) l (mm)

1 120 14.75 0.417 2.888

2 20 37.08 11.59 6.3662

3 120 47.75 0.417 9.351

4 20 37.08 11.59 6.3662

5 120 14.75 0.417 2.888

TLINE SCHEMATIC:-

After analyzing the circuit, S-parameters on a rectangular plot are as follow:

36

MLINE SCHEMATIC:-

37

MLINE PLOT:-

SONNET SCHEMATIC:-

38

SONNET PLOT:-

39

Example 3

AIM:-Design a low pass filter for fabrication using microstrip lines. The specifications are: cut off frequency of 4GHz, 3rd order, impedance of 50 Ω, and a 3 dB equal ripple characteristics.

For a 3rd order equal ripple filter,

g1= g3=3.3487, g2=0.7117

After applying Richard transformation and Kuroda identity final structure can be drawn as follow:

TLINE SCHEMATIC:-

40

After analyzing the circuit, S-parameters on a rectangular plot are as follow:

MLINE SCHEMATIC:-

41

MLINE PLOT:-

42

SONNET SCHEMATIC:-

SONNET PLOT:-

43

Example 4

AIM:-Design a low pass filter for fabrication using microstrip lines. The specifications are: cut off frequency of 4GHz, 5th order, impedance of 50 Ω, and a 0.5 dB equal ripple characteristics.

For a 5th order equal ripple filter,

g1=1.7058=g5, g2=1.2296=g4, g3=2.5408

44

After applying Richard transformation and Kuroda identity final structure can be drawn as follow:

TLINE SCHEMATIC:-

After analyzing the circuit, S-parameters on a rectangular plot are as follow:

MLINE SCHEMATIC:-

45

MLINE PLOT:-

46

SONNET SCHEMATIC:-

SONNET PLOT:-

47

48