How to Suppress Spurious Signals in Oscillator Design by Norbert H.L. Koster Bettina J. Koster Adalbert Beyer, Fellow IEEE Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 1 Overview Introduction The Oscillator Circuit CAD of the Oscillator Experiments on the Oscillator Spectral Lines Improving of the Circuit and Results Discussion Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 2 1 Introduction A technique entitled Fast Approximation Formulas Describing the Non-linear Intrinsic Transistor Equivalent Circuit Elements Speed Up and Improve the CAD of Oscillator Circuits was introduced in frame of the 2003 IEEE MTT IMS workshop marked by WSI in Philadelphia. That contribution has treated an important topic of oscillator design. During the last three years, new developments on this field justify a continuation of the presentation mentioned above. Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 3 Introduction Some Facts: Unwanted spurious signals appear in the oscillator’s spectrum when the oscillator circuit produces at least one additional signal than only the designed one. These additional signals interfere with the projected oscillation frequency or with its harmonics and produce a number of disturbing spurious signals. Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 4 2 Introduction What is to do? To avoid this problem it is necessary to analyze the reason for these additional oscillations and to take such measures as inhibiting the oscillator’ s circuit capability to produce additional parasitic oscillations. This presentation examines the problem of exciting spurious signal in an oscillator circuit and demonstrates, how an oscillator can be CAD designed and assembled, producing the desired frequency signal, only. Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 5 The Oscillator Circuit Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 6 3 CAD of the Oscillator In order to analyze the oscillator circuit, we use a program package from Stephen A. Maas and Arthur Nichols entitled „C/NL 2 for Windows 95, NTT and 3.1: Version 1.2 – Linear and Nonlinear Circuit Analysis and Optimization, Artech House Publishers, London, 1996. – ISBN 0-89006-899-2.” Although, this CAD tool is very compact and easy to use, it allows a very fast and effective implementation of all the necessary equations to calculate the voltage-dependent values of the intrinsic elements of both the JFETs during the tuning and analyzing sequence. Additionally, it is possible to insert easily a sufficient number of own equations directly into the CAD program. Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 7 CAD of the Oscillator The program uses nodal analysis similar to SPICE. The first task is to determine the variation of smallsignal parameters of the active elements as a function of dc operating (quiescent) point. Furthermore, it is necessary to predict the feasibility for oscillation. These problems were solved in the Philadelphia talk by using simple algebraic expressions for calculating those quantities. Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 8 4 CAD of the Oscillator DC Analysis (Source Coupled JFETs) VC RD Id1 T1 Vs = RS (I d1 + I d2 ) Vr Id2 T2 Vgs1 = Vgs2 = Vs Vgs2 Vds1 = Vc RS (I d1 + I d2 ) Vds1 Vds2 Vgs1 VS Vds2 = Vc RS (I d1 + I d2 ) Rd I d2 RS Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 9 CAD of the Oscillator Drain-Source-Voltage of JFET 1 5 V V f f ds1 = 0.9613 c 1.0246 (1 e 01 )(1 e 02 ) V V V R with the quantities f = 0.0303 S f02 = 1.385 VC 01 4 Rs 10 3 Id1 T1 Id2 Ur T2 Uds1 Uds2 Ugs1 Ugs2 Us 15 22 Uds1 / V Rd Ub 33 47 56 68 2 82 100 1 RS 0 1 2 3 4 5 Ub / V Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 10 5 CAD of the Oscillator Small Signal Equivalent Circuit of a JFET CPGD LG 1 RG Cgd g G ugs i ds Cgs ZL e , e , l e RD d Cds ZL a , a , l a s CPG 2 D Rds Rgs LD CPD RS i ds = ugs gm e-j LS 1' 2' S Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 11 CAD of the Oscillator Drain-Source-Capacitor C ds fF = 285,732 (1 e f13 ) 31,60106 Cgd g ugs d abbreviation: i ds Cgs Cds Rgs Rds s Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen i ds = ugs gm e-j f13 = 1,1569 U gs V Uni Gran Canaria, Las Palmas, 2007 + 1,483 U ds V 12 6 CAD of the Oscillator Drain-Source-Capacitor ugs Cgd d i ds Cgs Cds Rgs Rds s 200 Ugs / V 0,0 -0,2 -0,4 -0,6 Cds / fF g 300 -0,8 -1,0 -1,2 -1,4 100 i ds = ugs gm e-j 0 0 1 2 3 4 5 Uds / V Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 13 CAD of the Oscillator Remember, the JFETs used as active devices in this oscillator are the type of CFY30 from INFINEON Technologies AG. From there, all results given in this presentation refers solely to this type of JFET, but may be similar if comparable types are used. Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 14 7 CAD of the Oscillator The simulated magnitude of the complex Sparameter s11 is considered for a wide frequency range from dc up to 10 GHz. The analysis of the oscillator circuit gives some hints (parasitic elements) for additional oscillations in the upper GHz region. This seems to be the reason for the spurious oscillation. Next view graph shows the calculated course of the magnitude of the reflection coefficient s11 from dc to 10 GHz. Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 15 CAD of the Oscillator (Simulation of s11 at 4.0 Vdc Biasing) Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 16 8 Experiments on the Oscillator Circuit The Measurement Set Up Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 17 Experiments on the Oscillator Circuit The Measurement at a Voltage of 3.9 VDC Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 18 9 Experiments on the Oscillator Circuit The Measurement at a Voltage of 3.9 VDC Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 19 Spectral Lines To give some explanation for the number of the resulting spectral lines, we will regard the simple mixture of two sinusoidal voltages v1(t) and v2(t) with different frequencies f1 and f2. The non-linear context between the current i(t) and the signal voltage v(t) at an active element can be described approximately by a polynomial with the order of n = N n= N i (t ) = k n [v(t )]n . n =1 Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 20 10 Spectral Lines If the signal voltage v(t) is a superposition of two sinusoidal voltages with different frequencies and different amplitudes, it is valid: i =2 v(t ) = vi (t ) with i =1 vi = vˆ sin (2f i t ) for i = 1, 2 . Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 21 Spectral Lines After a little algebraic manipulation a result for the signal voltage v(t) having the following components may be obtained: 1) the two frequencies f1 and f2, 2) the harmonics 2 f1 , 3 f1, 4 f1, 2 f2, 3 f2 and 4 f2, 3) the mixtures of second grade f1 ± f2 4) the mixtures of third grade 2 f1 ± f2 and f1 ± 2 f2 and 6) the mixtures of fourth grade 3 f1 ± f2, 2 f1 ± 2 f2, f1 ± 3 f2. These are already the resulting frequencies assuming N = 4. More realistic is an amount of N of above 18, Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 22 11 Improving of the Circuit and Results in MHz Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 23 Improving of the Circuit and Results Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 24 12 Improving of the Circuit and Results in MHz Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 25 Improving of the Circuit and Results Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 26 13 Improving of the Circuit and Results Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 27 Discussion This paper has been shown that a number of additional signals can be excited by the oscillator’s active kernel due to parasitic effects. These interfere with the projected oscillation frequency or with its harmonics and produce a number of disturbing spurious signals. By means of a suitable CAD program, such as C/NL2, it is possible to avoid this problem. The CAD tool can analyze the reason for these additional oscillations and comfortably give advice how to take measures in order to inhibit the oscillator’s circuit capability to produce these unwanted additional parasitic oscillations. This talk examined the problem of exciting spurious signals in an oscillator circuit and proves that an oscillator can be easily CAD designed and assembled, producing the designed frequency signal, only. Prof. Dr.-Ing. A. Beyer Uni Duisburg-Essen Uni Gran Canaria, Las Palmas, 2007 28 14

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