narrow band microstrip filter design with ni mwo · pdf filedaniel g. swanson, jr. dgs...

Daniel G. Swanson, Jr.DGS Associates, LLC

Boulder, CO

[email protected]

www.dgsboulder.com

Narrowband Microstrip Filter Design With NI AWR

Microwave Office

Narrowband Microstrip Filters

Microstrip Filter Design 2

D. G. Swanson, Jr., “Narrow-Band Microwave Filter Design,” IEEE Microwave Magazine,

vol. 8, no. 5, pp. 105-114, Oct. 2007.

There are many topologies we can choose from.

The interdigital filter has been very popular.

But it has some design and fabrication challenges.

Microstrip Interdigital


y

x1 2 3 4 5

Standard metal pattern to via alignment spec is +/- 2 mils Interdigital at X-band requires something like +/- 0.2 mils

+y metal pattern misalignment

Resonators 1, 3, 5 get longer

Resonators 2 & 4 get shorter

The filter is badly mistuned

Microstrip Combline

Microstrip interdigital topology– Has been a workhorse for many years– Very compact in terms of wavelengths– Very sensitive to absolute via placement– Very sensitive to alignment of metal pattern to vias– Y-axis misalignment rapidly detunes filter

Microstrip combline topology– Has not been studied in detail– Also very compact in terms of wavelengths– True combline requires loading capacitors and extra vias– Microstrip combline is not pure TEM, allows longer resonator– All resonators are grounded at the same end– Y-axis misalignment should only shift center frequency



Conventional Combline

Resonators are typically 50 to 60 degrees long for moderate bandwidths.

For octave band filters resonators may be in the 30 degree range.

For narrow band filters resonators may be in the 70 to 80 degree range.

Some form of capacitive loading is used to achieve resonance.

If the medium is pure TEM, 90 degree long combline resonators do not couple.

30-80deg


Microstrip Combline

If we want to build a microstrip combline it is tempting to adopt the conventional topology.

But we need an extra set of vias for the capacitive loading. And we need to accurately realize the capacitive loading, possibly

with an interdigital capacitor structure to get significant loading.


10% BW Microstrip Combline

What if we arbitrarily throw away the capacitive top loading? Our first assumption is that resonators will be close to 90 degrees

long and we may not get much coupling. This assumes the vias are ideal short circuits, which of course

they are not. It also assumes a pure TEM environment, which microstrip is not. In fact, we can port tune this structure to be a 10% bandwidth filter.

15 mil alumina25 mil wide resonatorsL = 94 mils


Port Tuned Response


10% BW Microstrip Combline

After optimization, the printed parts of the resonators are 73 to 77 degrees long, depending on the assumed reference plane for the vias.

We have some capacitive loading due to the open end fringing.

And we have significant loading due to the finite inductance of the vias.

There is also some mutual inductance between the vias.

Compared to the conventional approach, this microstrip combline is both bottom loaded and top loaded.

73-77deg

Combline Filter Fabrication


Absolute via placement is still a problem with the combline

Metalized slot replaces vias Misalignment variables

– Slot or pattern Y-axis shift– Slot or pattern XY rotation

Efficient thin-film process Applied Thin-Film Products

www.thinfilm.com EM modeling is simpler

and faster without vias

Metalized slot


Microstrip Combline Example

N = 5 Microstrip Interdigital Center Frequency: 2.44 GHz Bandwidth: 244 MHz (10%) Insertion Loss: < 2 dB Return Loss: 20 dB (.044 dB ripple)


Design Flow Estimate order of filter and stopband rejection Choose waveguide channel dimensions

– Distributed filters couple to the waveguide channel Build model of proposed resonator (with loss)

– Compute available Qu– Estimate insertion loss

Build Kij design curve (no loss) Build Qex design curve (no loss) Build model of complete filter and apply port tuning Use port tuning corrections to refine filter dimensions Do final run of filter with loss turned on

– Verify insertion loss in passband– Verify rejection in stopbands


Chebyshev Lowpass Prototype

N is the lowpass or bandpass filter order. The gi’s are frequency and impedance scaled values for a

lowpass filter with a cutoff frequency of = 1 radian and a return loss of 20 dB.

Any given passband ripple / return loss level requires a unique table.

Other tables are available in the literature or the gi’s canbe computed.

Chebyshev Lowpass Prototype: 0.044 dB ripple, 20 dB return loss, 1.22 VSWRN g0 g1 g2 g3 g4 g5 g6 g7 g8 g9 g10 g1 - gN

2 1.0000 0.6682 0.5462 1.2222 1.2144

3 1.0000 0.8534 1.1039 0.8534 1.0000 2.8144

4 1.0000 0.9332 1.2923 1.5795 0.7636 1.2222 4.5727

5 1.0000 0.9732 1.3723 1.8032 1.3723 0.9732 1.0000 6.4989

6 1.0000 0.9958 1.4131 1.8950 1.5505 1.7272 0.8147 1.2222 8.4011

7 1.0000 1.0097 1.4368 1.9414 1.6216 1.9414 1.4368 1.0097 1.0000 10.4028

8 1.0000 1.0189 1.4518 1.9682 1.6570 2.0252 1.6104 1.7744 0.8336 1.2222 12.3447

9 1.0000 1.0252 1.4618 1.9852 1.6772 2.0662 1.6772 1.9852 1.4618 1.0252 1.0000 14.3710

Microstrip Qu


25mil (.635mm) thick aluminaassumed r = 9.8

50mil by 435mil(1.27mm by 11.05mm)

Vertical via metal

EMSightAWRDE V11

150 mil

25 mil600 mil

Microstrip Qu – From Group Delay


230


Midband Insertion LossChebyshev Lowpass Prototype: 0.044 dB ripple, 20 dB return loss, 1.22 VSWR

N g0 g1 g2 g3 g4 g5 g6 g7 g8 g9 g10 g1 - gN

2 1.0000 0.6682 0.5462 1.2222 1.2144

3 1.0000 0.8534 1.1039 0.8534 1.0000 2.8144

4 1.0000 0.9332 1.2923 1.5795 0.7636 1.2222 4.5727

5 1.0000 0.9732 1.3723 1.8032 1.3723 0.9732 1.0000 6.4989

6 1.0000 0.9958 1.4131 1.8950 1.5505 1.7272 0.8147 1.2222 8.4011

7 1.0000 1.0097 1.4368 1.9414 1.6216 1.9414 1.4368 1.0097 1.0000 10.4028

8 1.0000 1.0189 1.4518 1.9682 1.6570 2.0252 1.6104 1.7744 0.8336 1.2222 12.3447

9 1.0000 1.0252 1.4618 1.9852 1.6772 2.0662 1.6772 1.9852 1.4618 1.0252 1.0000 14.3710

dB 23.1230244.0

44.24989.6343.4

343.4)(

01

0

u

N

ii

Qf

fgfLoss

Loss will be higher at the band edges.


Dishal’s Method

As early as 1951, Milton Dishal [2] recognized that any narrow band, lumped element or distributed bandpass filter could be described by three fundamental variables:– the synchronous tuning frequency, f0

– the couplings between adjacent resonators, Kr,r+1

– the singly loaded or external Q, Qex

The Kij set the bandwidth of the filter and the Qex sets thereturn loss level.

For any narrowband filter (<10% bandwidth) we can compute the required Kij and Qex from the Chebyshev lowpass prototype.

The K and Q concept is universal and can be applied to any lumped element or distributed filter topology or technology [4,5].


Definition of Kij and Qex

0

12210

0

12

10

12

100

2

)(

fffBWfff

ggBW

ggfffK

BWgg

ffggfQ

jijiij

ex

f1 = bandpass filter lower equal ripple frequency

f2 = bandpass filter upper equal ripple frequency

f0 = bandpass filter center frequency

BW = percentage bandwidth

gi = prototype element value for element i

Note: Equations assume Qu is infinite.


Our Filter: N = 5, BW = 10%

393.91.09393.00.1

0643.07691.13577.1

1.0

0882.03677.19393.0

1.0

10

323,2

212,1

BWggQ

ggBWK

ggBWK

ex

Chebyshev Lowpass Prototype: 0.044 dB ripple, 20 dB return loss, 1.22 VSWRN g0 g1 g2 g3 g4 g5 g6 g7 g8 g9 g10 g1 - gN

2 1.0000 0.6682 0.5462 1.2222 1.2144

3 1.0000 0.8534 1.1039 0.8534 1.0000 2.8144

4 1.0000 0.9332 1.2923 1.5795 0.7636 1.2222 4.5727

5 1.0000 0.9732 1.3723 1.8032 1.3723 0.9732 1.0000 6.4989

6 1.0000 0.9958 1.4131 1.8950 1.5505 1.7272 0.8147 1.2222 8.4011

7 1.0000 1.0097 1.4368 1.9414 1.6216 1.9414 1.4368 1.0097 1.0000 10.4028

8 1.0000 1.0189 1.4518 1.9682 1.6570 2.0252 1.6104 1.7744 0.8336 1.2222 12.3447

9 1.0000 1.0252 1.4618 1.9852 1.6772 2.0662 1.6772 1.9852 1.4618 1.0252 1.0000 14.3710


Computing Spacings and Tap Height

Our resonator geometry is now fixed. We have enough Qu to meet the insertion loss goal. We have goals for the Kij’s and Qex Now we need to compute the spacings between

resonators and the tap height.

Computing Coupling Coefficients


Compute coupling coefficient as function of spacing between resonators.

Lossless model– Faster– No corrections to Kij

Via ports for tuning in our circuit simulator– MoM mesh may not be

perfectly symmetrical– Faster than making geometry

changes in the EM model

EMSightAWRDE V11

Computing Coupling Coefficients


150 mil

25 mil600 mil

EMSightAWRDE V11

Vertical via metal

Extracting Coupling Coefficients


0)))2,2(((0)))1,1(((

YimmagYimmag

We want to force synchronous tuning.

At resonance:

Loosely couplewith transformers.

Extracting Coupling Coefficients


-30 dB min

MHz 148Bandwidth Coupling

0607.0tCoefficien Coupling

12

0

12

fff

ff

Coupling Curve: Fit in Mathcad


29600.32903.11137.0 KKSpacing 150 mil

25 mil600 mil

Computing Qex


Tune to center frequency at Port 2. Measure reflected group delay at Port 1. Tap height sets the return loss level

of our filter. Note this resonator is longer than the

resonators used to compute couplings.

Port Tuned Reflected Delay


98.92

605.244.21416.34

)nS()GHz(2

ex

dex

Q

tfQ Tap_Height = 93 mils

Qex Curve: Fit in Mathcad


2410498.40158.02012.0 DelayDelayHeight Tap 150 mil

25 mil600 mil

First Iteration Geometry


S1 = 31 milsS2 = 47 mils

L1 = 442 milsL2 = 437 mils

Tap Height = 97 mils

Default Meshing


First Iteration Response


4350 UnknownsAFS Sweep

15 Frequencies

150 mil

25 mil600 mil

Arbitrary Channel Height Change


100 mil

25 mil600 mil

Internal Ports for Port Tuning


Internal nodes

External port

Tuning element

Low error Very effective for

frequency tuning Limited to lumped

elements by the transformer

How do we tune couplings?

Impact of Internal Ports


Port Tuning With Internal Ports


110

ij

i

jiijij

KL

LLKM

Add negative offset inductors so coupled L’s don’t go negative.

Coupled inductor array

Dummy element

“zero tuning” = +20 pH

Mutual couplings

Mutual couplingstune EM circuit couplings

Custom symbol

Port Tuning with EQR_OPT


General purpose optimizers may work fine for low order filters, but they can be inefficient for more complex filters.

EQR_OPT_MWO is a dedicated optimizer for microwave filters.

It finds an exact equal ripple response with a very small number of iterations.

It communicates with Microwave Office via the COM interface.

It works on any Chebyshev filter thatcan be defined in Microwave Office.

We can also use it to port tunean S-parameter file from anyEM simulator.www.swfilterdesign.com

Second Iteration: Port Tuned


X X X X X

X EM simulation frequencies

What Do The Tunings Tell Us?


Center resonator tuning is almost perfect(remember “zero” is +20 pH)

The outer resonators want to be longer The first and last gaps want to be smaller The inner gaps want to be larger Return loss tells us the tap position wants

to move down very slightly The resonator and coupling tunings

will interact The general strategy is to go after the

largest errors at each step

Next step: Resonators 1, 2, 4, 5 each one mil longerMove tap down one mil

Third Iteration


Fourth Iteration


Resonator tunings are all pretty close The first and last gaps want to be smaller The inner gaps want to be larger Return loss is perfect

Next step: First and last gaps one mil smallerInner gaps one mil larger

Fifth Iteration


Coupling corrections are small and in the numerical noise (note opposite signs)

Resonator tunings have shifted We need less than a full one mil change

in resonator length and resonator spacing.

Next step: Fine tune open endsFine tune couplings

Fine Tunings


Add and subtract bits of metal at the open ends to fine tune the resonators.

Adding or subtracting metal at the base of the resonators fine tunes the coupling.

Reso 1 Reso 2 Reso 3

We have to go back and forth a little between

frequency and coupling adjustments.

Final Tuning


If we set the tunings to zero and see very little movement in the response we are done.

Next step is to remove the tuning ports and do a twoport analysis of the filter.

Two Port EM Simulation


Summary

Dishal’s K and Q method leads us to a simple design flowfor narrowband filters.

We can modernize the method by using EMSight to buildthe Kij and Qex design curves that we need.

We can then build a complete model of our filter in EMSight, port tune it and get a very good prediction of performance.

These virtual prototypes in our EM simulator avoid thetime and expense of multiple hardware prototypes.

Experience has shown that we can rely on theEM simulator models.



References

[1] R. Levy, R. Snyder and G. Matthaei, “Design of Microwave Filters,” IEEE Trans. Microwave Theory Tech., vol. MTT-50, pp. 783-793, March 2002.

[2] M. Dishal, “Alignment and adjustment of synchronously tuned multiple resonate circuit filters,” Proc IRE, vol. 30, pp. 1448-1455, Nov. 1951.

[3] M. Dishal, “A simple design procedure for small percentage bandwidth round-rod interdigital filters, IEEE Trans. Microwave Theory Tech., vol. MTT-13, pp. 696-698, Sept. 1965.

[4] J. Wong, “Microstrip tapped-line filter design,” IEEE Trans. Microwave Theory Tech., vol. MTT-27, pp. 44-50, Jan. 1979.

[5] D. G. Swanson, Jr., “Narrow-Band Microwave Filter Design,” IEEE Microwave Magazine, vol. 8, no. 5, pp. 105-114, Oct. 2007.

[6] D. G. Swanson, Jr., “Corrections to “Narrow-Band Microwave Filter Design, “ IEEE Microwave Magazine, vol. 9, no. 1, p. 116, Feb. 2008.

narrow band microstrip filter design with ni mwo · pdf filedaniel g. swanson, jr. dgs...

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