High frequency signal filter

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Introduction to high frequency filter

by

Nam Tran Pham

Robert Bosch Center for Micro and Power Electronics

Reutlingen

November 19, 2012


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Abstract

In the modern communication system, the higher data rate and transmission

speed are required. As the result, the frequency of the signal becomes higher.The traditional method to design a filter becomes unsuitable to handle highfrequency signal. This short study is written with the intention to give thereader a small aspect of designing signal filter for high frequency system. Somebasic understanding about high frequency signal and the method to handle theproblem along with samples are discussed.


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Contents

Table of contents I

List of figures II

Abbreviation III

1 Introduction to signal filter 11.1 Fundamental types of filters . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Low pass filter . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2 High pass filter . . . . . . . . . . . . . . . . . . . . . . . 21.1.3 Band pass filter . . . . . . . . . . . . . . . . . . . . . . . 21.1.4 Notch filter . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Design of fundamental filter . . . . . . . . . . . . . . . . . . . . 41.2.1 Design requirement of filter . . . . . . . . . . . . . . . . 41.2.2 Filter realization . . . . . . . . . . . . . . . . . . . . . . 41.2.3 Fundamental filter overview . . . . . . . . . . . . . . . . 5

2 High frequency signal filter 6

2.1 Parameters of high frequency signal and system . . . . . . . . . 62.1.1 Wavelength of high frequency signal . . . . . . . . . . . . 62.1.2 Reflexion and scattering parameter models . . . . . . . . 8

2.2 Filter with micro strip lines . . . . . . . . . . . . . . . . . . . . 92.3 IQ-Modulation for Transmitter . . . . . . . . . . . . . . . . . . 12

2.3.1 Simple modulation method . . . . . . . . . . . . . . . . . 122.3.2 IQ-Modulation . . . . . . . . . . . . . . . . . . . . . . . 12

2.4 High frequency filter conclusion . . . . . . . . . . . . . . . . . . 14

Bibliography 15

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List of Figures

1.1 Ideal frequency response of low pass filter . . . . . . . . . . . . . 11.2 Ideal frequency response of high pass filter . . . . . . . . . . . . 21.3 Ideal frequency response of band pass filter . . . . . . . . . . . . 21.4 Ideal frequency response of notch filter . . . . . . . . . . . . . . 31.5 Low pass filter with different realization methode . . . . . . . . 4

1.6 Ideal frequency response of allpass filter . . . . . . . . . . . . . . 52.1 Capacitor and inductor model at radio-frequency . . . . . . . . 72.2 Insertion loss of capacitor [Murata-Data sheet] . . . . . . . . . . 72.3 Measurement the 220nF capacitor . . . . . . . . . . . . . . . . 72.4 Simple principle of S-Parameter system . . . . . . . . . . . . . . 82.5 Smith Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.6 Transformation with capacitor and inductor . . . . . . . . . . . 102.7 Transformation with micro strip line . . . . . . . . . . . . . . . 102.8 Schematic of matching network . . . . . . . . . . . . . . . . . . 102.9 PCB Artwork of matching network and measurement comparison 11

2.10 Principle working of simple modulation method . . . . . . . . . 122.11 Blockdiagramm des IQ Modulator am Sender . . . . . . . . . . 132.12 Spectrum of IQ-modulators output signal with 85o Phase-Shift 14

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Abbreviation

DAC . . . . . . . . . . . . . . . . . . . Digital Analog ConverterEMI . . . . . . . . . . . . . . . . . . . . Electromagnetic interferenceGBW .. . . . . . . . . . . . . . . . . . Gain BandwidthPCB ..... . . . . . . . . . . . . . . . Printed Circuit BoardSAW . . . . . . . . . . . . . . . . . . . Surface Acoustic Wave

UHF . . . . . . . . . . . . . . . . . . . Ultra-High Frequency

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1 Introduction to signal filter

1.1 Fundamental types of filters

In this section the ideal fundamental types of filters will be introduced. Thecommon filter characteristics, basic applications and some design parameters

of those filters will be discussed.

1.1.1 Low pass filter

The low pass filter is the most well known and used filter in the electronic field.The frequency response of a ideal low pass filter is given in Figure 1.1. Thebasic parameters for a low pass filter are:

The Bandwidth B. The gain factor in Pass-band 0 B.

Zero gain in Stop-band > B.

Figure 1.1: Ideal frequency response of low pass filter

A low pass filter is often used to smoothen the signal, to block the high fre-quency distortion in DC supply network or as stabilize-element in controllingsystem.

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CHAPTER 1. INTRODUCTION TO SIGNAL FILTER

1.1.2 High pass filter

Figure 1.2: Ideal frequency response of high pass filter

In Figure 1.2 is the frequency response of a ideal high pass filter. As theopposite of low pass filter, the basic parameters for a high pass filter are:

The cut-off frequency B.

The pass band gain |H()|.

The attenuation in stop band: < B.

The high pass filter is often used to couple AC-signal into the system, or

connection link for AC-signal between different systems.

1.1.3 Band pass filter

Figure 1.3: Ideal frequency response of band pass filter

The band pass filter is a combination between high pass and low pass filter,its frequency response is shown in Figure 1.3. The basic parameters of a idealband pass filter are:

Filters band-width B.

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Center frequency o

Gain within filter passband: |H()|, (o B2 ) (o + B2 ).

Attenuation in stop-frequency.

Resultantly quality factor: Q = oB

The band pass filter is widely used in communication system to filter the signalbefore up-link and to select the desired signal as well as to reduce noise on thedown-link.

1.1.4 Notch filter

The last type of the fundamental filter is the notch filter. As the frequencyresponse in Figure 1.4 describes, the notch filter is normally used to preventunwanted frequencies to interfere with the system like in the EMI-Filter or toprevent the interference between the signals of one system. The basis param-eters of the notch filter are:

The stopband bandwidth B.

Center notch frequency

o.

Stopband attenuation factor H(o)/H(0).

Symmetrical in gain factor between low and high pass band.

Figure 1.4: Ideal frequency response of notch filter

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1.2 Design of fundamental filter

1.2.1 Design requirement of filter

All of the filters can be described with a transfer equation between the inputand output. This function describes the relationship between the voltage orcurrent of input and output signals, which depends on the frequency of thesignal.

The transfer function of a filter must satisfy the Hurwitz condition forthe stability.

The filter with passive elements, the input and output impedances mustbe positive real for realization.

Lossless filter is desirable to minimize any signal power loss, and reduc-tion of noise level.

1.2.2 Filter realization

The fundamental filter can be realized with passive components as show in

Figure1.5(b), or with a active components like in Figure 1.5(a).

(a) Active filter (b) Passive filter

Figure 1.5: Low pass filter with different realization method

The method using passive components is more suitable for filter in high fre-quencies. They produces less noise than the active components, and the max-imum working frequency of a opamp in active filter is limited, this factor de-terminates by the GBW. The circuit topology of passive filter do not usuallyhave a feedback, therefore more resistant against instability. But at the lower

frequency the active filter shows many advantages over passive filter:

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The active filter has great potential with integrated circuit technology.

Active filter has good isolation between input and output ports.

Active filter can be used as filter and amplifier.

1.2.3 Fundamental filter overview

In this chapter the fundamental filters were introduced with their applicationsand design parameters. These filter are used in combination with each othersto create the needed character of signal filter. There is other type of filter, inwhich the signal level of input and output signal are the same, but the phase

are changed, the frequency response is shown in Figure1.6. In the high fre-quency application, which wireless communication is a typical example, wherethe bandwidth of signal is often limited and most of the system are optimizedfor only one small frequency area, therefore the most mentioned filter is thebandpass filter. Other than the filtering application, the design of filter has

Figure 1.6: Ideal frequency response of allpass filter

to concern about the impedance matching aimed toward maximizing signalpower transfer between source and load. For example, in the communicationvia satellites the signal levels at receiver are usually very weak, so the inputfilter of the receiver has to be optimized in order to get as much signal poweras possible. This also requires that the filter network has to be lossless, sincethe passive filter can not amplifier the signal. The active filter is often un-suitable for these applications, because they tend to be considerably noisierthan the passive counterparts. In the communication channel, where the sig-nals are really closely packed together, the linearity of the front-end filter isvery critical. The non-linearity of a filter may cause potentially unacceptable

intermodulation responses, in this criteria the passive architectural filter isbetter.

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2 High frequency signal filter

2.1 Parameters of high frequency signal and

system

2.1.1 Wavelength of high frequency signal

The phase velocity of a electromagnetic wave is defined as in 2.1, in whichc0 3 108[m/s] is the speed of light and r is the relative dielectric constant ofthe medium material. As the result the wavelength of a electromagnetic wave isgiven in 2.2. With the increasing of frequency the wavelength becomes smaller.At UHF-band between 300MHz and 3GHz, vacuum as medium material thewavelength is between 1 meter to 0.1 meter. With the semiconductor materialGermanium r = 16.6 the wavelength is from 0.2 meter to 0.02 meter. Thephysical sizes of components and the strip conductors in the electrical circuit

are larger than the wavelength itself, hence the electromagnetic can change itsphase many times between the input and output of one component or stripline. This results unpredictable circuits behavior.

vp[m/s] =c0

r(2.1)

[m] =vpf

(2.2)

At higher frequency, the influent of parasitic elements of components becomemore significantly, the model for the discrete component becomes more com-plex, as shown in Figure 2.1. The conductor path between the components,because of the phase change between input and output, becomes a electricalpart of the circuit schematic. All the discrete components of a electrical circuithave to be considered as distributed elements. Each capacitor and inductorhas a self-resonant frequency, where capacitor becomes inductor and inductorbecomes capacitor because of the parasitic capacitor and inductor. Figure 2.2illustrates the insertion loss of capacitor depend on frequency,the lowest peakof insertion loss denotes the self-resonant frequency of capacitor. In Figure2.3is a measurement result of a 220 nF capacitor, the result shows that at 900MHz the capacitor is already a inductor.

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CHAPTER 2. HIGH FREQUENCY SIGNAL FILTER

(a) Capacitor RF model (b) Inductor RF model

Figure 2.1: Capacitor and inductor model at radio-frequency

Figure 2.2: Insertion loss of capacitor [Murata-Data sheet]

Figure 2.3: Measurement the 220nF capacitor

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2.1.2 Reflexion and scattering parameter models

Because of the reasons mentioned in section2.1.1 it is difficult to characterize

a network of filter in high frequency system. The unavoidable parasitic induc-tance in circuit interconnects makes perfect short circuits an impossibility athigh frequency. The attempt based on open-short measurement is not suitable,the measurement results might be compromised by the parasitic componentsof the measurement equipments.At high frequency a circuit network is usually characterized by the scatteringparameter models. In contrast to the impedance and admittance, the scatter-ing parameters of linear electrical network are measured without need of open-short circuiting input and output port. Instead, these ports are terminated infixed and known characteristic impedance that are often similar or identicalto the terminating impedances incorporated in the design. The S-Parametersare not only measurement-friendly but also useful in design. Because the S-Parameter of a linear network interrelate incident and reflected waves of energyat input and output port, they are useful in the design of microwave network.The reason is, at high frequency the voltages and currents are more difficult toquantify. By optimizing the refection of input and output of the network thenetwork can be aimed to be lossless and delivers the maximum signal powertransfer from source to load.

In figure2.4 is the simple model of a two port system. The S-Parameter of a

Figure 2.4: Simple principle of S-Parameter system

two port system is given in equation 2.3, a1, b1, a2, b2 are the input and outputincident and reflected energies, respectively. To determinate the coefficientsof S-Matrix, the reflexion factor at the input and output are calculated as inequations 2.4 and 2.5.

b1b2

=

S11 S12S21 S22

a1a2

(2.3)

1 =Zin RsourceZin + Rsource

(2.4)

2 =Zout RloadZout + Rload

(2.5)

As the result, the S-Parameter Matrix of a two port system is shown in equation2.6.

S11 S12S21 S22

= 1 1 + 1

1 + 2 2

(2.6)

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2.2 Filter with micro strip lines

As mentioned in section 2.1.1, the electrical path between the components,

so called micro strip lines, can not be considered as a short connection. Thephases of traveling wave signals, between input and output of micro strip lines,can be very different. Using this character, a micro strip line can be used asactive part of a filter architecture. One of the most used tool to design filterusing micro strip line is Smith chart. Normally the system, which is designedwith smith chart, is called transformation network. This system also has theselective property, which is specified for one small bandwidth and one pair ofimpedances at its input and output.

In Figure 2.5 is the basic of smith chart, one impedance value can placed

on this chart by using the reflexion factor or normalized value on referenceimpedance, typical 50. According to the position of the impedance on thischart, the structure of transformation network will be determinated along withother requirements. The effect of one component in the transformation networkis shown in Figure 2.6. As mentioned before, the micro strip line causes thephase change of the signal, this mechanism of this effect can be explained usingthe transformation in figure 2.7.

Figure 2.5: Smith Chart

With the smith chart method of network design, the effects of every circuitcomponents are clearly visualized, hence the accuracy of the circuit is bet-ter. Depends on the tolerance of the component, the architecture of the sys-tem can be changed to remain the integrity of the result. In figure2.8 is theschematic of a matching network, designed to match a 50 input impedanceand a (10.5j 6.6) output impedance at 900MHz. The micro strip lines weredesigned to compensate the 20% tolerance of the capacitor. The measure-ment comparision in figure 2.9(a) shows a quite good match between simulationand hardware, even with simple method of PCB etching.

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Figure 2.6: Transformation with capacitor and inductor

Figure 2.7: Transformation with micro strip line

Figure 2.8: Schematic of matching network

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(a) Reflexion loss (b) Matching network

Figure 2.9: PCB Artwork of matching network and measurement comparison

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2.3 IQ-Modulation for Transmitter

2.3.1 Simple modulation method

In high frequency system, the base frequency signals normally have to be mod-ulated with a higher frequency carry signal before transmission. Because mostof the DAC have a limited maximum frequency of MHz, and the required fre-quency for wireless communication is in GHz area, therefore a analog mixer isneeded to boost the frequency of base-band signal to carry-band signal. Buteven a ideal analog mixer has its drawback, this is shown in equation 2.7, theoutput signal of a mixer consists of two signals. The frequencies of those signalsare different, but the information within them is the same, therefore to savethe cost of bandwidth only one signal is needed to be transmit. As the result,at the output signal of frequency mixer has to be filtered with a bandpass, thisprinciple is demonstrated in Figure 2.10.

y = cos( t) cos( t)=

1

2[cos(t t) + cos(t + t)] (2.7)

In application for wireless communication this method encounters a majorproblem, the carry frequency is normally many times higher then the base

frequency, therefore the different between and + is very small. Designa bandpass filter at high frequency, which blocks only one signal without effectsthe other signal, is a engineering challenge.

2.3.2 IQ-Modulation

The principle of a IQ-Modulator is shown in Figure 2.11. The input signal ofmodulator is splitted in two components I and Q, the I component is calledIn-Phase signal and the Q component is Quadrature signal. The Q signal isshift 90o degree compared to I signal. The LOI and LOQ signals are the carry-band frequency signal with 90o phase difference. The equations 2.8, 2.9 and2.10 show that the output signal contains only one frequency.

Figure 2.10: Principle working of simple modulation method

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P hase shift

Mixer

LOI

Mixer

LOQ

input xI

xQ

output

Figure 2.11: Blockdiagramm des IQ Modulator am Sender

xI =cos(t)

LOI =cos(t)

xI LOI =cos(t) cos(t)=

1

2[cos(t t) + cos(t + t)] (2.8)

xQ =cos(t +

2) = sin(t)

LOQ =cos(t +

2) = sin(t)

xQ LOQ =sin(t) sin(t)=

1

2[cos(t t) cos(t + t)] (2.9)

y =xI LOI + xQ LOQ = cos(t t) (2.10)

With the IQ-Modulation method, a bandpass filter is no longer needed, andthe system proofs to be robust against errors and mis-matched due to thecomplexity. A simulation was made, with the phase shift between the I-Signaland Q-Signal only 85o, as the result in figure 2.12 the level difference betweenthe pass frequency and stop frequency is still more than 40dB.

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Figure 2.12: Spectrum of IQ-modulators output signal with 85o Phase-Shift

2.4 High frequency filter conclusion

Section 2.1 provides the basic understanding of signal and its properties in ahigh frequency system. The problem with the physical size of the electrical

components leads to the different way of handling and designing the high fre-quency filter. The S-Parameter system, introduced in section 2.1.2, is a specialmethod to work with high frequency system. By using the S-Parameter andsmith-chart, designer is able to predict the behavior of the electrical compo-nents and the affection of parameter tolerance as well as parasitic elements.The design method in section 2.2 is one of the typical way of designing a highfrequency filter. But on the mobile communication devices, where the size ofthe device is smaller than the required place for micro strip-line filter, there isanother method to realize a filter, one of them is using acoustic wave propertyof signal on carrier material, like in SAW-Filter. Apart from normal electrical

filter, there is also filter-alike configuration, the method with IQ-Modulation insection 2.3 is one of them. By using the mathematical relation of the signals,designer can create a system with a filter property.

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Bibliography

[1] F. Caspers. Rf engineering basic concepts: The smith chart, 2010. [Online;accessed 23-October-2012].

[2] J. Choma. Radio frequency filter design, 2013. [Online; accessed 23-October-2012].

[3] Wikipedia. Smith chart wikipedia, the free encyclopedia, 2012. [Online;accessed 23-October-2012].

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High frequency signal filter