Qucs - A Tutorial

1 QucsA TutorialSubcircuit and Verilog-A RF Circuit Simulation Models forAxial and Surface Mounted ResistorsMike BrinsonCopyrightc 2014 Mike Brinson, Centre for Communications Technology, LondonMetropolitan University, London, is granted to copy, distribute and/or modify this document under theterms of the GNU Free Documentation License, Version or any later versionpublished by the Free Software Foundation. A copy of the license is included inthe section entitled GNU Free Documentation License .IntroductionResistors are one of the fundamental building blocks in electronic circuit most instances conventional resistor circuit simulation models are characterizedby I/V characteristics specified by Ohm s law. In reality the impedance of RFresistors is frequency dependent, being determined by component physical prop-erties, component manufacturing technology and how components are connectedin a circuit.

2 At low frequencies fixed resistors have a nominal value at room tem-perature and can be modelled accurately by Ohm s law. At RF frequencies thefact that a resistor acts more like an inductance or a capacitance can play a cru-cial role in determining whether or not a circuit operates as designed. Similarly,if a resistor is modelled as an ideal component at a frequency where it exhibitssignificant reactive properties then the resulting simulation data are likely to beincorrect. The subcircuit and Verilog-A compact resistor models introduced inthis qucs note are designed to give good performance from low frequencies to RFfrequencies not greater than a few Resistor ModelsThe schematic symbol, I/V equation and parameters of the qucs linear resistormodel are shown in Figure 1. In contrast to this model Figure 2 illustrates thestructure of a printed circuit board (PCB) mounted metal film (MF) axial RFresistor (a), its qucs schematic symbol (b) and its equivalent circuit model (c).

3 Athin film surface mounted (SMD) resistor can also be represented by the modelshown in Figure 2 (c). At signal frequencies where the largest dimension of an axialor SMD resistor is less than approximately 20 times the smallest signal wavelengtha resistor can be modelled by a lumped passive circuit consisting of a resistorRsin series with a small inductanceLswith the combination shunted by parasiticcapacitorCp. In Figure 2 Rsis the nominal value of a resistor at its parameterextraction temperatureTnom,Lsrepresents the inductance associated withRswhere the value ofLsis largely determined by the trimming method employedduring component manufacture to set the value ofRsto a specified , capacitorCpmodels a parasitic capacitance associated withRswherethe value ofCpis a function of the physical size ofRs.

4 At RF frequencies it isimportant, for accurate operation, to add lead parasitic elements to the intrinsicequivalent circuit model shown within the red box draw in Figure 2. In Figure 2 LleadandCshuntrepresent resistor series lead inductance and shunt capacitanceto ground respectively. A typical set of model parameters for a 51 5 % MF axialresistor are (1)Ls=8nH,Cp=1pF,Llead=1nH andCshunt= Illustrated inFigure 3 is a basic S parameter test bench circuit for measuring the S parameters1 Figure 1: qucs built-in resistor 2: PCB mounted resistor: (a) axial component mounting, (b) qucs symboland (c) equivalent circuit an RF resistor over a frequency range 1 MHz to GHz. This example alsodemonstrates how the real and imaginary parts of a resistor model impedance canbe extracted from S parameter simulation data.

5 The graphs in Figure 3 clearlydemonstrate that the impedance of the typical MF RF resistor described in pre-vious text and modelled by the equivalent circuit shown in Figure 2 is a strongfunction of frequency at higher frequencies in the band 1 MHz to 3: qucs S parameter simulation test circuit and plotted output data for aMF axial resistor:Rs=51 ,Ls=8nH,Cp=1pF,Llead=1nH andCshunt= of the RF resistor modelA component level version of the proposed RF resistor model is shown in Figure4, whereZ1 =j Llead(1)Z2 =Rs+j Ls (1 2 Cp Ls) j Cp Rs2(1 2 Cp Ls)2+ ( Cp Rs)2(2)Z3 =j Llead(1 2 Llead Cshunt)(3)Zseries=Z1 +Z2 =Rseries+j Xseries(4)Zb=Zseries||XCshunt=Zseries(1 +j Cshunt Zseries)=ZBR+j ZBI,(5)Z=j Llead+Zb=ZR+j ZI.(6)Figure 5 illustrates how a set of theoretical equations can be converted into Qucsequations for model simulation and post simulation data processing.

6 In this exam-ple qucs equationEqn1holds values for RF resistor model parameters and QucsequationEqn2lists the model equations introduced at the start of this 5 also gives a set of cartesian graphs of post simulation output data which3 Figure 4: RF resistor model rotated through 90 degrees and connected with oneterminal grounded, similar to the test circuit in Figure 3. Sections of the modelare shown grouped for calculation of the model impedance howZRandZI, and other calculated items, vary with frequency overthe range 1 MHz to 5: Theoretical analysis of RF resistance impedance Z using qucs postprocessing facilities: note a dummy simulation icon, in this example DC simulation,is required to force qucs to complete the analysis measurement of RF resistor impedance us-ing a simulated impedance meterA simple impedance meter for measuring the real and imaginary components ofcomponent and circuit impedance, using small signal AC simulation, is shownin Figure 6.

7 The impedance measuring technique uses a 1 Amp AC constantcurrent source applied to one terminal of a two port electrical network. The secondterminal is grounded. A parallel high resistance resistor (1E9 in Figure 6) shuntsthe network under measurement to ensure that there is always a direct current pathto ground as required by the qucs simulator during the calculation of simulationresults. If required the 1 Amp AC source can be set at a lower value. In such casesthe value ofVResmust also be scaled to give the network 6: A simple qucs test circuit for demonstrating the use of an AC constantcurrent source to measure electrical network of RF resistor data from measured SparametersIn the past the cost of Vector Network Analyser systems for measuring S pa-rameters has been prohibitively expensive for individual engineers to , this scene is changing with the introduction of low cost systems like theDGSAQ Vector Network Analyser (VNWA)1.

8 This instrument operates over afrequency band width of GHz, providing a range of useful functions with high-est accuracy at frequencies up to 500 MHz. This form of VNWA is particularlysuited to Radio Amateur requirements and qucs users interested in RF circuitanalysis and design. Such equipment is ideal for measuring RF circuit S param-eters and providing measured data for subcircuit and Verilog-A compact devicemodel parameter extraction. Shown in Figure 7 is a graph of measured S pa-rameter data for a nominal 47 resistor2. As well as displaying, and printing,measured data the DGSAQ Vector Network Analyser software can output datatabulated in Touchstonec SnP 3file format. These files can be read by Qucsand their contents attached to an S parameter file icon for inclusion in circuit1DG8 SAQ VNWA 3 & 3E- Vector Network Analysers, SDR Kits Limited, Grangeside BusinessCentre, 129 Devizes Road, Trowbridge, Wilts BA14-7sZ, United Kingdom, DG8 SAQ VNWA 3 & 3E- Vector Network Analysers- Getting Started Manual for Win-dows 7, Vista and Windows diagrams.

9 Figure 8 shows this process as part of an RF resistor modelparameter extraction technique involving DGSAQ VNWA measured S parameterdata and qucs simulated S parameter data. The brown Test circuits box showstest circuits for firstly reading and processing the DGSAQ VNWA measured datalisted in file , and for secondly generating simulated S parameter datafor an RF resistor specified by parametersLs=L,Cp=C,Llead=LL,Cshunt= , andRs= . Presented in Figure 9 are the qucs Optimization controls which are used to set the range of L, C and LL values that optimizer ASCO willselect from to obtain the best fit between the measured and simulated S parameterdata. Note in this parameter extraction system that S[1,1] refers to measured Sparameter data and S[2,2] to simulated S parameter data. Two least squares costfunctions calledCF1andCF2are used as targets in the minimisation forCF1andCF2can be found in the red box called Simulation Con-trols.

10 In this parameter extraction example the least squares cost functionCF1is employed to minimize the square of the difference between the real values of theS parameters and least squares cost functionCF2is employed to minimize thesquare of the difference between the imaginary values of the S parameters. Qucspost-simulation processing is also used to extract values for the real and imaginarycomponents of the RF resistor impedance. Both the S parameter data and theimpedance data are displayed as graphs in Figure 8. Notice in this example theSPICE optimizer ASCO is used to find the values ofL,CandLLwhich mini-mize CF1 and CF2. Also note thatRsandCshuntare held at fixed values duringoptimization. In the case ofRsits nominal value can be found from DC or low fre-quency AC measurements.