V I S H AY I N T E R T E C H N O L O G Y, I N C . Resistive Products Application Note AP0010 Resistors in Microwave Applications D u e to t h e r apid ly i nc re a si ng nu mb er of h ig h frequency applications, the resources below 1 GHz are becoming scarce. For this reason the frequency range up to and above 40 GHz is becoming more and more important, and thus also the need to understand the frequency characteristics of passive components in microwave ﬁeld. Special HF-Resistors Needed The number of high frequency applications is rapidly increasing today. Consequently the need for resistors with good high frequency performance is growing. Former measurements [1] conﬁrm the expectation that the usual helical trimming of a cylindrical resistor causes increased inﬂuence of reactances at high frequencies. This effect can be reduced by means of a special pulsed trim. The following illustration (Figure 1) shows the comparison between a helical trimmed MINI-MELF resistor (size 0204) and the pulsed trimmed version. The difference is signiﬁcant. www.vishay.com 1 MMA 0204 HF Frequency Figure 1. MMA 0204 vs. MMA 0204 HF Theoretically a resistor is frequency-independent. Actually there is an additional contribution to the impedance by an inductance L and a capacitance C to the actual resistance value R. The inductance results from the trim cutting, the capacitance is formed by the ceramic dielectric of the resistor body and the metallic contacts. The following substitution circuit is used to describe the resistance behavior (Figure 2). The capacitors Ci are formed by integrating the resistor into the circuit. Figure 3 presents the trim cuttings of different resistors. On the top there is the well known helical trim cutting with its comparatively high inductance of up to 22 nH [1]. At C Ci R L Ci Figure 2. Resistor substitution circuit VSD-AP0010-0504 A PPL I CAT I O N N OT E Some years ago 500 MHz was an "ultra" high frequency. Nowadays frequencies up to 2 GHz are nothing special. Mobile phones operate in the 900 MHz frequency range (GSM) and 1,8 GHz (DCS) respectively. The DECT-standard will become more and more important, it is based upon 1,8 GHz too. By using this standard the telecom providers do not need to install an expensive telephone line to each telecom customer. For mass applications there are satellite TVreceivers working at frequencies between 10 and 12 GHz and an intermediate frequency up to 2 GHz. Last but not least ISM applications, for example wireless LANs, become more and more important. Most popular bands are 430 MHz and 2 GHz today, but also the 5 GHz band is increasingly used. IZ/IR In this paper, the high frequency behavior of chip resistors sizes 0805 and 0603 will be shown from 0,1 to 20 GHz. A comparison with special trimmed cyl i ndr ical resistors si zes 0204 and 0102 w i l l be taken. First the conditions for a good high frequency p e r for m a n c e w i l l b e d e mon st r at e d . T h e p ap e r continues with an analysis of the inf luence of the calculated parasitics in the substitution circuit. Plots of the test data of the high frequency characteristics complete the representation. MMA 0204 Application Note AP0010 Resistive Products Resistors in Microwave Applications scattering parameters by a vector network analyzer. This measuring device determines ratios of incident, transmitted and reﬂected waves. In our case there are two important scattering parameters: the input reﬂection coefﬁcient S11 and the transmission coefﬁcient S21. Helical Trim S11 is the ratio of the reﬂected to the incident wave, and S21 the ratio of the transmitted to the incident wave respectively. Pulsed Trim Results Resulting data determined by a vector network analyzer are real and imaginary part of S11 and S21. There are two possible calculating methods for the impedance: Meander Trim 1. The magnitude of the reﬂection coefﬁcient is calculated to the centered picture there is the special HF trim cutting as further trim for cylindrical resistors. The typical meander trim cutting of ﬂat chip resistors is shown on the lower drawing. According to [2] the complex input reﬂection coefﬁcient of a series resistor is Requests for High Frequency Performance S11= A PPL I CAT I O N N OT E For high frequency applications, there are other demands more i mpor t ant than toleranc e and temp erature coefﬁcient. 1. For most of the practical applications, the resulting deviation of the impedance Z up to |Z| / R = 1,2 may be disregarded. For higher deviations, the resistor is not acceptable or the occurring reactances have to be regarded into the circuit. 2. The working frequency has to be far below the resonance frequency. Near the resonance minor changes in working frequency cause major changes in impedance – the circuit is likely becoming instable. 3 Computer simulation is an easier way to design microwave circuits. Therefore, the resistor must be able to be modelized by a simple model. 4. High frequency characteristics must be reproducible in series production in order to avoid individual trimming of print boards by the manufacturer. (1) S11 = Re {S11}2 +Im {S11}2 Figure 3. Trimming of MELF, MELF HF and Chip Z Z+2gZ 0 (2) where Z 0 =50Ω Result of combining these two equations is: Z= 2gZ 0 g S11 1– S11 (3) Z 50Ω f ~ ~ ~ Incident and Transmitted Wave 50Ω Reﬂected Wave Measuring High Frequency Performance How to measure inductance and capacitance at microwave range? The only way to get the required data is to measure www.vishay.com 2 Figure 4. Reﬂection and transmission measurement For technical support, contact [email protected] Document Number: AP0010 Revision 19-Apr-05 Application Note AP0010 Resistive Products Resistors in Microwave Applications To compare different resistance values it is necessary to standardize IZI by referring it to the actual resistance R. 2,0 MCU 0805 1,5 MCT 0603 |Z|/R The other way to calculate IZI by using S21 is: 2. The magnitude of the transmission coefficient is calculated to S21 = Re {S21}2 +Im {S21}2 1,0 MMA 0204 HF and MMU 0102 HF (4) 0,0 100MHz Frequency According to [2], the complex forward transmission coefﬁcient of a series resistor is: S21= Z0 1 Z0+ Z Figure 5. |Z|/R for 50 Ω-resistors (5) Modelling and Simulation 2 Result of combining equations (4) and (5) is: Z =2gZ 0 g 1– S21 S21 (6) The measurement and calculation results are shown at ﬁgures 6 to 9 at the last two pages. The considered resistance range is 6,8 Ω up to 470 Ω. These are the most important resistance values for today’s microwave engineering. In principle there is the same qualitative behavior valid for all styles and sizes. A lot of microwave circuits are designed by using simulation programs. The simulation considers the internal inductance and capacitance. It is possible to apply the resistor at frequencies wh ich would otherwise be not acceptable due to the variations of impedance. For the resistor model the above mentioned substitution circuit is used. Analyzing the circuit results in the following equation for the complex impedance Z: L R Z=Rg 1–ω 2LC+jωRC 1+jω (7) Because ω2LC is a very small value it can be disregarded for most of the practical cases. Now the frequency characteristic depends only on the ratio of L/R to R•C. In the case they are equal the impedance of the resistor is frequency independent. In the following table some examples are pointed for the required L for a given C in dependency of R. This overview is useful to getting a feeling for the dimensions of C and L. MCT 0603 and MMU 0102 HF For technical support, contact [email protected] R C 6,8 Ω 50 Ω 470 Ω 35 fF 35 fF 35 fF L = R2 • C 0,0016 nH 0,875 nH 7,7 nH www.vishay.com 3 A PPL I CAT I O N N OT E 1. The inductance predominates for resistance values up to approximately 75 Ω for MELF size and 120 Ω for chip size. The resonance frequency is above 20 GHz. 2. The capacitance characterizes resistance values greater than the above mentioned. There are differences between styles and sizes in detail. 1. By using the same trim cutting the high frequency behavior becomes better for smaller body dimensions of the resistor. 2. Comparing the trim cuttings the special pulsed trim cutting of MELF resistors is better than the standard meander trim cutting of ﬂat chip resistors. As an example a comparison is made for 50 Ω resistors in the diagram above. There is demonstrated that the meander trim causes a higher inductivity than the pulsed trim of cylindrical HF sizes. However, the high frequency behavior of ﬂat chip resistors is much better than that of helical trimmed cylindrical resistors. Document Number: AP0010 Revision 19-Apr-05 10GHz 20GHz 1GHz Application Note AP0010 Resistive Products Resistors in Microwave Applications In order to calculate the magnitude of the impedance based on equation (7), the numerator and the denominator will be handled separately. Z =Rg L 1+ ω R S11< =tan 2 1+ (ωRC ) (8) 2 The following table contains some determined values of capacitance and impedance: C L MCT 0603 6,8 Ω 50 Ω 470 Ω 35 fF 35 fF 35 fF 0,58 nH 1,0 nH 1,53 nH MMU 0102 HF 6,8 Ω 50 Ω 470 Ω 35 fF 35 fF 35 fF 0,2 nH 0,41 nH 2,37 nH A PPL I CAT I O N N OT E Up to now this method takes into account only the magnitude of the impedance. The necessary next step is to calculate phase angle by using equation (7). www.vishay.com 2 Im {S11} Re {S11} (9) Comparing measured with calculated data quantiﬁes the substitution circuit completely. By using this equation, it is possible to plot the |Z|/R characteristics over the considered frequency range. Comparing measured data with calculated graphs, allows to determine the reactances of the substitution circuit. R The phase angle is deﬁned as Conclusions The very good high frequency performance of special trimmed HF MELF resistors and standard meander trimmed f lat chip resistors qualify these components for microwave applications for more than 5 GHz depending on actual requirements. For best microwave c h a r a c t e r i st i c s , MICRO -MELF MMU 0102 HF is the first choice. For mass applications up to 3 GHz f lat chip resistors MCT 0603 and MCU 0805 are applicable without problems. Nevertheless, for better HF characteristics it is possible to optimize actual ﬂat chip resistors. Further miniaturization will also offer better HF performance. Bibliography / References [1] Laurich, W.: SMD Resistors Beyond UHF, CARTS - EUROPE 1990, page 41 [2] Meinke/Gundlach: Taschenbuch der Hochfrequenztechnik, Springer Verlag, page C11 For technical support, contact [email protected] Document Number: AP0010 Revision 19-Apr-05 Application Note AP0010 Resistive Products Resistors in Microwave Applications 2,0 6,8 Ω 50 Ω 27 Ω 1,5 |Z|/R 100 Ω 1,0 220 Ω 470 Ω 0,5 100MHz 1GHz 10GHz 20GHz Frequency Figure 6. |Z|/R for MCT 0603 2,0 50 Ω 1,5 |Z|/R 100 Ω 1,0 220 Ω 0,5 100MHz 1GHz 10GHz 20GHz Frequency Figure 7. |Z|/R for MCU 0805 Document Number: AP0010 Revision 19-Apr-05 For technical support, contact [email protected] www.vishay.com 3 A PPL I CAT I O N N OT E 470 Ω Application Note AP0010 Resistive Products Resistors in Microwave Applications 2,0 6,8 Ω 27 Ω |Z|/R 1,5 50 Ω 1,0 100 Ω 220 Ω 470 Ω 0,5 100MHz 1GHz 10GHz 20GHz Frequency Figure 8. |Z|/R for MMU 0102 HF 2,0 6,8 Ω 27 Ω A PPL I CAT I O N N OT E |Z|/R 1,5 50 Ω 1,0 100 Ω 220 Ω 470 Ω 0,5 100MHz 1GHz 10GHz 20GHz Frequency Figure 7. |Z|/R for MMA 0204 HF www.vishay.com 2 For technical support, contact [email protected] Document Number: AP0010 Revision 19-Apr-05 Application Note AP0010 Resistive Products VISHAY AMERICAS VISHAY ELECTRONIC GMBH ONE GREENWICH PLACE SHELTON, CT 06484 UNITED STATES PH: +1-402-563-6866 FAX: +1-402-563-6296 GEHEIMRAT-ROSENTHAL-STR. 100 95100 SELB GERMANY PH: +49-9287-71-0 FAX: +49-9287-70435 VISHAY INTERTECHNOLOGY ASIA PTE LTD. VISHAY S.A. 25 TAMPINES STREET 92 KEPPEL BUILDING #02-00 SINGAPORE 528877 PH: +65-6788-6668 FAX: +65-6788-0988 VISHAY JAPAN CO., LTD. GE EDISON BUILDING, SHIBUYA 3F 3-5-16 SHIBUYA SHIBUYA-KU TOKYO 150-0002 JAPAN PH: +81-3-5464-6411 FAX: +81-3-5464-6433 4, RUE DE SALONIQUE 95101 ARGENTEUIL FRANCE PH: +33-1-39-98-22-00 FAX: +33-1-39-98-22-05 VISHAY LTD. PALLION INDUSTRIAL ESTATE SUNDERLAND, SR4 6SU GREAT BRITAIN PH: +44-191-514-4155 FAX: +44-191-567-8262 One of the World’s Largest Manufacturers of Discrete Semiconductors and Passive Components Document Number: AP0010 Revision 19-Apr-05 For technical support, contact [email protected] www.vishay.com 5 A PPL I CAT I O N N OT E WORLDWIDE SALES AND TECHNICAL SUPPORT Resistors in Microwave Applications

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