Laboratory #2: Introduction to Microstripline Transmission Lines, Reflection and Transmission Coefficients, and S-Parameters

Transcription

1 EEE 7 La # Laratry #: Intrductin t Micrstripline Transmissin Lines, Reflectin and Transmissin Cefficients, and -Parameters I. OBJECTIVE A micrstrip transmissin line is designed fr nminally 50Ω. The reflectin and transmissin characteristics are measured and cmpared t thery. -parameters are derived. II. INTRODUCTION Micrstriplines are cmmnly used in printed circuit ards (PCB) t cnnect electrical and electrnic cmpnents. They are als used t create circuit functins such as filters thrugh special layut arrangements. A crssectinal vie f a micrstripline is shn in Figure. Cnductr Dielectric h Grund Plane Figure. Crssectinal Vie Of A Micrstripline The design equatins fr the characteristic impedance f a micrstripline are: Narr strips (/h ): 8h 60ln + 4h Ω, () ε 0 r + εr h + + Wide strips (/h ): 0π 6 h h + + h ε 0 r + εr h + + Ω. ()

2 EEE 7 La # The underlying assumptin is that the metal cnductrs are significantly thinner than the dielectric. Metal thicknesses f 37 mils ( inches) is typical fr z. cpper plating. Plating refers t the numer f unces f metal depsited n a flat surface per square ft. The ard is made f FR-4 (r G-0) material ith a nminal relative dielectric f 4.5. In radi frequency (RF) and micrave (µ-ave) circuits, the characteristics impedance f the micrstriplines are carefully cntrlled t prevent unanted signal reflectins caused y dissimilar impedances. As the speed f digital circuits increase, the intercnnectins eteen digital cmpnents must e carefully designed t eliminate unanted signals caused y reflectins. One cmmn methd fr measuring the reflectin and transmissin characteristics f any device under test (in this case a micrstripline) invlves the using a netrk analyzer. A netrk analyzer alls cnvenient measurements f signal reflectin and transmissin in a variety f frmats. It can measure signal delay, phase, and gain f the device under test (). All f these measurements are made ith respect t the surce and terminal impedance f the netrk analyzer. The default impedance f the HP875A netrk analyzer is set at 50 Ω. The signal reflected frm the is usually measured as a rati t the incident signal. It can e expressed as reflectin cefficient r return lss. These measurements are descried mathematically as, reflec ted per Erefl Reflectin cefficient ρ (magnitude nly) incide nt per Einc Γ (Reflectin magnitude and phase) (3) Return lss (db) 0 lgρ (4) tanding Wave Rati WR + ρ ρ (prnunced "sir" as in sirl) (5) Displaying the reflectin measurement in plar frm n the netrk analyzer ith a marker alls direct determinatin f the cmplex impedance f the. The center f the circle represents a cefficient Γ f 0 (a perfect match, n reflected signal). The utermst circumference f the scale represents a Γ f (00% reflectin). The phase angle is directly read frm the display. The magnitude and phase ill e directly displayed in the marker data readut fr any frequency. The amunt f per reflected frm a device is directly related t the impedances f the and the measurement instrument. Γ 0 ccurs hen the and the analyzer have identical impedances. A shrt circuit has Γ 80. Every ther value f Γ crrespnds uniquely t a cmplex device impedance. In terms f impedances, Γ, (6) +

3 EEE 7 La # 3 here is the impedance f the measurement instrument, is the impedance f the. T facilitate cmputatins, the nrmalized (in this case nrmalized t 50 Ω) impedance is, N + Γ Γ. (7) -parameters are cmmnly used t characterize high frequency circuits. -parameters (r cattering-parameters) asically are t-prt characteristics f the. Additinally, insight int the ehavir f traveling aves are readily deduced frm -parameters. -parameters can readily e fund using the schematic f the test set-up shn in Figure. -Prt Netrk L E i E i E r E r Figure. T Prt Netrk Used Fr -Parameter Measurements Define ne variales ith respect the a characteristic impedance f the measurement instrument, a Ei, a Er, Ei, Er. (8) -parameters relates these fur aves as flls: a + a. (9) a + a Fr, the utput prt f the is terminated (ith 50 Ω) and the rati f t a is measured,

4 EEE 7 La # 4 a a 0. (0) Terminating the utput prt f the ith the impedance f the measurement instrument is equivalent t setting a 0 since a traveling ave incident n this lad ill e ttally asred. is the input reflectin cefficient f the. The frard transmissin thrugh the is the rati f t a. This culd either e the gain f the amplifier r the attenuatin f a passive netrk, a a 0. () By terminating the input side f the netrk, e set a 0 and can then measure the utput reflectin cefficient,, and the reverse transmissin cefficient,, defined as, and a a 0 a a 0, (). (3) -parameters are typically expressed as a magnitude and phase. III. PROCEDURE A. Calirate the Netrk Analyzer Caliratin f the netrk analyzer may e necessary due t the many adapters and MA pigtails used. B. Determine the Transmissin and Reflectin Cefficients f the Filters Prvided Plt the magnitudes f the transmissin cefficient, reflectin cefficient, and WR f the circuits ver a frequency range that clearly shs the passand and the stpand. Find the nminal,, and WR f the circuits in the passand and the stpand. Determine the impedance f the circuits in the passand and the stpand. C. Design a Micrstripline Design a micrstripline using the ard and cpper tape prvided. Determine the theretical impedances f a micrstripline cnstructed frm the sizes f cpper tape prvided.

5 EEE 7 La # 5 Cnstruct t micrstriplines f different impedances. Design ne f the micrstriplines t e nminally 50 Ω. D. Measure the Micrstripline Determine the transmissin and reflectin cefficients f the t micrstriplines cnstructed. Plt the magnitudes f the transmissin cefficient, reflectin cefficient, and WR f the micrstriplines. Find,, and WR f the micrstripline at 55 MHz, 330 MHz, and GHz. Determine impedances f the micrstriplines at 55 MHz, 330 MHz, and GHz using the measured reflectin cefficients. E. Cmment On Yur Results