RF & Microwave Measurement Lab

Report No. 2

February 2010

Passive Low-Pass RF Filter Design

Daniel Smith

Rodrigo Quinteros

Sahand Noorizadeh

1 Introduction

When designing a simple microwave circuit, passive components such as resistors, capacitors and

inductors are very useful for quick construction. However, these components have many parasitic

elements such as shunt capacitance or parallel resistance that have a large impact on the overall

circuit performance at microwave frequencies. In order to properly simulate a circuit, these para-

sitic elements can be modeled and compensated for in the design. Measurements using a Vector

Network Analyzer (VNA) of the passive components can be used to create the model.Using this

parasitic model design, a simple lumped element filter can be accurately designed and simulated.

This report is concerned with extracting models for the available family of inductors and

capacitors, designing and simulating a low-pass filter (LPF) using ideal components, optimizing

the LPF design, fabricating, and measuring its performance.

2 Design Approach

The design requirements of the 3-pole π network LC low-pass filter of this project are listed in

Table 1. To design the LPF with the specifications of Table 1, an inductor and capacitor were

Table 1: Design Specifications

Insertion Loss <0.5 dB at f = 0.1-2.0 GHz

Return Loss <15 dB at f = 0.1-2.0 GHz in 50 Ω systemStopband Rejection >7 dB at f = 3.8-4.0 GHz

>15 dB at f = 5.7-6.0 GHz

Physical size 0.2 in. x 0.3 in. MAX

modeled for this design using a one port PCB. The effects of the transmission line on the PCB were

neutralized by creating a short circuit on the board and adding port extensions on the VNA. Next,

the return loss (S11) parameter of both components was measured by placing the components on

the board in a shunt position. These parameters were exported from the VNA. Agilents Advanced

Design System (ADS) was the selected tool to simulate the design model of the capacitor and

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inductor. The S11 measurements that were taken of each component were imported into ADS as

a .S1P object, which means ADS creates a black box with the given S11 characteristics. A quick

simulation verified that the S11 parameters of the black box matched those from the VNA. The

models of the inductor and capacitor were constructed as a 1-port device with rough guesses as

to their approximate values. Using ADSs simulation and optimization routines, the values of the

parasitic components in the models were adjusted so that the S-parameter characteristics of the

model matched those of the measured component values from the VNA. When the s-parameters

were matched as close as possible, the values of the parasitic components were saved as the model.

The low pass filter was then constructed in ADS using the two models as derived above. The

parasitic values stayed the same, but the nominal values of the capacitors and inductor were varied

until the design specifications of the filter were met.

3 ADS Simulation and Results

After de-embedding the standard ±10% test capacitor and inductor with values of 1.6 nF and 4.0

nH and recording their S11 parameter over the frequency range of 1.0-4.0 GHz with 15 MHz step,

the measured S11 parameters were imported into ADS as a .S1P block to be used as a reference

to extract the parasitic values of the inductor and capacitor. These parasitic values were assumed

to be the same for all the available components from the same family. Therefore, the goal of

simulation was to use the extracted parasitic values and vary the nominal values of the inductor

and capacitors to achieve the design goal.

Figure 1 shows the circuit diagram of the non-ideal models that were used in ADS to extract

the parasitic vales.

Similar to the de-embedding process, port 2 of the non-ideal model circuits of the capacitor

and the inductor in ADS were grounded to form a 1-port device. The initial values of the parasitic

components were approximated based on circuits theory and experience. For example, the series

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(a) Non-ideal model of the capacitor. (b) Non-ideal model of the inductor.

Figure 1: Non-ideal models used in ADS simulation.

resistance of the inductor was initiated to 1Ω and was set to vary from 0.1Ω to 15Ω. All parasitic

capacitors were initiated to 1 pF and were set to vary from 0.01 pF to 100 pF. Two optimization

goal were used in the ADS optimization process. One for the magnitude and another one for

the phase of the S11 of the models. Both optimization goals were the same for the capacitor and

the inductor model. The goals were set to optimize for no more than 1 dB difference between

the imported dB(|S11|) and the model’s dB(|S11|) and no more than 5 difference between the

imported ∠S11 and the model’s ∠S11. All parasitic components were set to vary except for the 1.6

nF capacitor and 4.0 nH inductor. Figure 2 shows the measured S11 and the optimized S11 of the

models of circuits in Figure 1.

These optimized models of the capacitor and the inductor were used to construct a 3-pole π

network low-pass filter shown in Figure 3

The last step in designing the filter with specifications listed in Table 1 was to optimize the

filter circuit by varying the nominal values of the components (i.e. the core capacitance of the

capacitor and the core inductance of the inductor) and keeping the parasitic values derived pre-

viously constant. To do this, two optimization processes for frequency ranges of 1-2 GHz and

2-4 GHz were used. Each optimization process included one goal for the insertion loss (S21) and

another goal for the return loss (S11) to meet the design specifications. Figure 4 and Figure 5 show

the optimized results of the filter design in ADS.

The filter design optimization returned 4.0 nH for the inductor and 1.0 pF for both capacitors.

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(a) Capacitor. Red line: measured S11. Blueline: optimized S11.

(b) Inductor. Red line: measured S11. Blue line:optimized S11.

Figure 2: Optimization results.

Figure 3: 3-pole π network low-pass filter.

4 Measurement Data

The designed low-pass filter was fabricated with two 1.0 pF SMD capacitor and a 4.0 nH SMD

inductor. The properties of the substrate were unknown. Figure 6 shows the fabricated circuit.

The insertion and return losses of the fabricated designed low-pass were measured using a VNA

with 2-port calibration. Figure 7 shows the measurement results.

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Figure 4: Optimized insertion loss (S21).

Figure 5: Optimized return loss (S11).

Figure 6: Fabricated low-pass filter.

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(a) Measured insertion lossS21.

(b) Measured return lossS11.

(c) Measurement of all S-parameters.

Figure 7: Measurement results of the designed and fabricated LPF.

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5 Discussion

The optimization results to extract the parasitic components of the capacitors turned out out very

accurate and as shown in Figure 2 the modeled S11 had a slight deviation from the measured S11.

However, this deviation became considerably larger for higher frequencies near 4.0 GHz because of

an abrupt change in the measured S11 plot. This behavior could have been due to some frequency

dependent resistance that was not included in the model. Suspicion for a frequency dependent

resistance was motivated due to the fact that for the most part of the deviated curve, the real part

of S11 was shifted and imaginary part followed the expected trend. This deviation also existed in

the measured S11 of the inductor and this, too, could have been caused by a frequency dependent

resistance. To include this behavior in the model, a resistor can be added in series with the inductor

and the capacitor model whose value would be a function of frequency in the form of power series.

In general, the simulation results showed that the capacitor model was a good approximate.

The S11 of the inductor model shown in Figure 2 did not follow the measured S11 plot. First, it

was thought that the optimization range of the series parasitic resistor was not large enough but

increasing its range did not change the results. Different inductor models were also tried but none of

them were able to shift the molded curve lower. The deactivation or change of the limit of the phase

matching goal in ADS optimization did help lower the molded curve but with completely different

set of Im(S11) (i.e. rotated curve around the center of Smith chart). After many unsuccessful

attempts, it was decided to use the modeling results of Figure 2.b. The simulation results of the

inductor model showed that it needs additional parameters to more accurately model the inductor.

The optimization results of the filter shown in Figure 4 and Figure 5 showed that the a 4.0 nH

inductor and two 1.0 pF capacitors with the parasitic values that were extracted can be used to

fabricate a π network LC low-pass filter to meet the specifications listed in Table 1.

The measurements of the fabricated LPF shown in Figure 7 showed that the specifications

of the return loss were met. However, the insertion loss over the range of 0-2.0 GHz did not

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remain less than 0.5 dB. At f = 2.0GHz, the insertion loss was approximately 0.85 dB which

was off by 0.5 dB from the simulation results. The SMA and transmission line could have had a

small contribution to this loss. Also, the unmodeled parasitic component of the inductor that was

discussed earlier could have been a contributer as well. The latter case is more convincing because

the curve of the inductor model was constantly lower by a considerable value of the real part of

the S11 which is the resistance. Measurements showed that other specifications were met.

At low frequencies (f <2.0 GHz), the insertion loss graph shown in Figure 5 was smooth with a

resonance at f ≈ 2.0 GHz but the measurements showed multiple resonances in the same frequency

range. This could have been caused by noise with maximum amplitude as high as -30 dB. The noise

was not simulated in ADS which could have slightly changed the simulation results but not by a

considerable amount. Another reason could have been the reflection from the transmission lines

that were also not included in the ADS simulation. The transmission line at certain frequencies

where the measured S11 has maximums and minimums might have had large enough electrical

length that was capable of doing periodic matching and mismatching the input impedance of the

filter and the source. Although the length of the transmission lines to port 1 and port 2 were

not exactly the same but their difference was small enough to produce almost the same reflection

coefficients (S11 ≈ S22).

As shown in Figure 5.c, S11 and S22 were almost identical. So were S21 and S12. This meant

that the 2-port LPF was a symmetrical 2-port device.

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6 Conclusion

De-embedding is a useful technique to change the plane of reference and measure the S-parameters

of a single component. One method of extracting parasitics of a component is using its measured

S-parameters. ADS can be used to import measured S-parameters of a component and construct

and simulate its non-ideal model. Knowledge of parasitic components of a component is essential

in achieving accurate design and simulation before the fabrication.

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