Agilent EEsof EDA.

Transcription

1 Agilent EEsof EDA This document is owned by Agilent Technologies, but is no longer kept current and may contain obsolete or inaccurate references. We regret any inconenience this may cause. For the latest information on Agilent s line of EEsof electronic design automation (EDA) products and serices, please go to:

2 Lange Coupler Design Introduction: The Lange coupler is a four port, interdigitated structure deeloped by Dr. Julius Lange around The couplers are widely used as power combiners and splitters in RF amplifiers as well as in mixers and modulators. The coupling is deried from closely spaced transmission lines, such as microstrip lines. Typically the number of conductors or fingers (N) is een. The geometry for N = 4 is shown as Figure 1. Isolated Port (3) Direct Port (4) Bridge width (W2) Conductor width (W) Conductor spacing (S) Conductor Length (L) Width at port (W1) Input Port (1) Coupled Port (2) Figure 1. Lange Coupler Geometry The length of the fingers (L) is set by the desired center frequency (f o ) of the filter. The deice is relatiely broadband, with flat frequency response around f o. The finger length is equal to the quarter waelength ( λ s ) of f o in the substrate, i.e. L = λ s / 4 where: λ s = f o c ε eff ε eff = effectie dielectric constant c = 3 x 10 8 m/s (speed of light )

3 The effectie dielectric constant is a function of the dielectric constant of the substrate as well as its thickness (h) and the conductor width (w) and thickness (t).the waelength ( λ s ) can also be computed as the aerage of the waelengths of the odd and een modes. The coupler is usually designed for 3 db of coupling between the input port (1) and the coupled (2) and direct ports (4). The phase angles of the coupled signals are 90 degrees out of phase with the input near the design frequency. The design requirements could be specified as: S 21 > db for [ ( f o - f ) < f < ( f o + f ) ] for f = 0.25 f o S 41 > db for [ ( f o - f ) < f < ( f o + f ) ] for f = 0.25 f o For such a splitter, the theoretical maximum coupling is 3 db in each channel, i.e. half power. These coupling characteristics are most sensitie to the gap width (s) and the metal thickness (t) for a gien number of fingers (N). The characteristics of the substrate are also a factor. The requirements for return loss (S 11 ) and transmission to the isolated port (S 13 ) are commonly set less than some threshold in a frequency range ( f) about f o. For example: S 11 < -15 db for [ ( f o - f ) < f < ( f o + f ) ] for f = 0.25 f o S 31 < -15 db for [ ( f o - f ) < f < ( f o + f ) ] for f = 0.25 f o The phase of the isolated port and return loss and approximately zero and -180, respectiely. The other two parameters inoled are the width of the bridge wire (W2) and the conductor width at the port (W1) as defined in Figure 2. The width at the port is usually set by the associated circuit. The conductor width can be selected for characteristic impedance near 50 ohms. The bridge wire configuration is determined by manufacturing considerations. Coupler performance is relatiely insensitie to either parameter. Linear models proide a fast, accurate method of performing design trades and system optimization. The following sections describe the nature of the new linear model and its associated layout. The performance of the model will be compared with an electromagnetic simulation using this layout.

4 New Linear Model: The GENESYS enironment proides both a linear model and a corresponding layout for EM simulation. This model is a four-port deice using linear models of coupled lines. The schematic symbols for Lange Couplers with 4, 6 and 8 fingers are shown in Figure 2. Each coupler has the same set of parameters: (W, S, L, W1, W2). MLANG MLANG6 MLANG Figure 2. Schematic Symbols for Lange Couplers. The internal representation of the element is a combination of accurate linear models of coupled lines. The schematic of Figure 3 was employed for the example which follows. MLANG W=2 mil S=1 mil L=100 mil W1=10 mil W2=1 mil (3) 3 4 (4) (1) 1 2 (2) Figure 3. GENESYS Schematic for Example (N = 4)

5 GENESYS will automatically generate a corresponding layout by simply choosing Add Layout by right clicking on Designs\Models on the Workspace Tree. Be sure that the appropriate schematic is selected. For this example, the layout is shown in Figure 4. Leads with a width of 10 mils were added to this model. Ports are positioned at the ends of these leads in preparation for an EMPOWER simulation. Figure 4. Layout for Lange Coupler Example. Example: The coupler design with four fingers shown in Figure 4 has the following parameters: W = Width of each conductor (finger) = 2 mils G = Space between conductors (fingers) = 1 mil L = Length of fingers = 100 mils N = Number of fingers = 4 W1 = width at port = 10 mils W2 = bridge width = 1 mil Substrate Definition ε r = Dielectric constant = 9.6 t = Metal thickness = 0.2 mils tand = Loss tangent = Sr = Surface roughness = ρ = Resistiity = 1. h = Height = 10 mils

6 The magnitudes of the s-parameters for the linear model are shown in Figure 5a. The design frequency was 12.0 GHz, and the frequency range of interest was ± 3.0 GHz for a total range of 9.0 to 15.0 GHz. Using the design goals for coupling and return loss/isolation of 3.5 db and 15 db, respectiely, it is obsered that the coupling is within ± 10% of the goal. At 12 GHz, both S 21 and S 41 are approximately 3.3 db. At the extremes of frequency range, the coupling drops to around 3.7 db. The optimization features of GENESYS can be used to refine this design if necessary. The phase characteristics are displayed as Figure 5b. As expected, phase of the coupled signals is 90 with respect to the input, whereas the return loss and isolation signals are 180 and 0, respectiely. A comparison with another adanced simulation linear model (Figure 6) indicates consistent coupling characteristics. The return loss and isolation responses show significant differences een at low frequencies. On the other hand, the GENESYS linear model will be shown to be more consistent with electromagnetic simulations. The electromagnetic simulation (EMPOWER) was employed to generate comparable data. The magnitudes of the s-parameters for the linear model and EMPOWER simulation are compared in Figure 7. Notice that differences are small for the coupled parameters. At 12 GHz, the differences are: Linear model: S 21 = db S 41 = db EMPOWER: S 21 = db S 41 = db The EM simulation shows higher losses for isolation and return loss, particularly at higher frequencies. The linear model yields a somewhat more conseratie design. Design Issues: Changes in any of the design parameters affects the all of the s- parameters. For a four-port deice, this makes design trades more difficult. The impacts of these design ariations can readily be ealuated using linear models. Consider the design example. To increase the isolation at 12 GHz, the parameters might be aried one at a time and the impact on all s-parameters obsered. This is easily accomplished in GENESYS by making the desired parameters tunable. Simply place a question mark (?) in front of the parameter alue in the dialog box. For Lange couplers, these quantities also include the substrate properties, such as substrate height (h), dielectric constant ( ε r ) and metal thickness (t). As each parameter is changed, the graph is updated accordingly. The other major parameter is the number of fingers. If the number of fingers is increased from 4 to 8, and other parameters are adjusted slightly, the resulting response is as shown in Figure 8. The coupling response has become flatter oer a wide range of frequencies, but the coupling is lower. This may be a useful tadeoff in some applications.

7 Another approach to the design process is to use the optimization features of GENESYS. The parameters to be aried are made tunable as described aboe. These parameters are listed in Setup Variables dialog box under the toolbar Actions. The user has the option of applying limits to each ariable. For this example, the following ranges were used: [ 3 < ε r < 12 ], [ 5 < h < 20 ], [ s, unlimited ] Under Optimization Goals the following entries were made: S 21, S 41 > db from 9 < f < 15 GHz weight = 1.0 S 11, S 31 < -15 db from 9 < f < 15 GHz weight = 0.1 Although the optimization could not satisfy the optimization goals within the defined parameter space, obsering the graph as the optimization proceeded yielded the following insights: 1. Achieing greater than 3.5 db of coupling in both channels simultaneously oer a wide range of frequencies will be difficult. 2. The return loss and isolation can be improed significantly with a few parameter changes. These changes were: a. substrate height (h): 10 to 30 mils b. conductor spacing (s): 1 to 3 mils c. conductor width (w): 2 to 3 mils The frequency response resulting from these changes (Figure 9) indicates the isolation is on the order of 24 db compared to 15 db for the initial design. It was also obsered that if the ratio (s/h) = 0.1 is maintained, and the ratio of width to spacing is in the range of 1 to 2, then the coupling is approximately 3db ± 20% and independent of ariations in s, w, and h. This allows the isolation and return loss to be controlled as shown in Figure 10. Gien a design requirement for isolation, a range of alues of width, spacing and substrate height can be selected which meet that requirement.

8 Figure 5a. Magnitude of S-parameters for Linear Model d 1b b 2d d 3b 1) 9000 MHz a) db b) db c) db d) db 2) MHz a) db b) db c) db d) db 3) MHz a) db b) db c) db d) db DB[S11],DB[S21],DB[S31],DB[S41] a 1c 2c 2a 3c 3a DB[S11] DB[S31] DB[S21] DB[S41] Freq (MHz)

9 90 60 Figure 5b. Phase of S-parameters for Linear Model ) MHz a) b) c) a ANG[S21],ANG[S31],ANG[S41] b 1c ANG[S21] ANG[S41] ANG[S31] Freq (MHz)

10 0 Figure 6a. Comparison of Linear Models (Coupled Ports) -3-6 DB[S21],DB[S41],AdSim.Data.DB[S21],AdSim.Data.DB[S41] GENESYS ( ) Other Adanced Simulator ( ) -18 Linear model ( ) EM simulation ( ) -21 DB[S21] AdSim.Data.DB[S21] DB[S41] AdSim.Data.DB[S41] Freq (MHz)

11 0 Figure 6b. Comparison of Linear Models (Isolated Ports) -6 DB[S11],DB[S31],AdSim.Data.DB[S11],AdSim.Data.DB[S31] Linear ( ) EM ( ) GENESYS ( ) Other Adanced Simulator ( ) -30 DB[S11] AdSim.Data.DB[S11] DB[S31] AdSim.Data.DB[S31] Freq (MHz)

12 DB[S11],DB[S12],DB[S13],DB[S14],EM1.MLANG_4.DB[S11],EM1.MLANG_4.DB[S12],EM1.MLANG_4.DB[S13],EM1.MLANG_4.DB[S14] Figure 7. Comparison of Linear and EM Models Linear ( ) EM ( ) 1f 1b 1d 1h 1c 1a 1e 1g Freq (MHz) DB[S11] DB[S12] DB[S13] DB[S14] EM1.MLANG_4.DB[S11] EM1.MLANG_4.DB[S12] EM1.MLANG_4.DB[S13] EM1.MLANG_4.DB[S14] 1) MHz a) db b) db c) db d) db e) db f) db g) db h) db

13 DB[S21],DB[S41],Linear1.MLANG_8.DB[S21],Linear1.MLANG_8.DB[S41] Figure 8. Sensitiity to Number of Fingers (N = 4, 8) b 1a a 2b N = 4 N ( = 4 ( ) ) N = 8 N ( - = (- -) ) b 3a 1d 3d 2c 1c 3c 2d Optimization goal for S13 and S11 1) 9000 MHz a) db b) db c) db d) db 2) MHz a) db b) db c) db d) db 3) MHz a) db b) db c) db d) db DB[S21] DB[S41] Linear1.MLANG_8.DB[S21] Linear1.MLANG_8.DB[S41] Freq (MHz)

14 Figure 9. S-parameters After Optimization d 1b b 2d d 3b 1) 9000 MHz a) db b) db c) db d) db 2) MHz a) db b) -3.1 db c) db d) db 3) MHz a) db b) db c) db d) db DB[S11],DB[S21],DB[S31],DB[S41] Optimization Goal for S31 and S c 1a 2c 2a 3c 3a -33 DB[S11] DB[S31] DB[S21] DB[S41] Freq (MHz)

15 Figure 10. Sensitiity of Isolation to Various Parameters -30 (w/s) = 1-25 w = 2 w = 3 w = 4-20 Isolation, S13 (db) -15 (w/s) = 2-10 Conditions (s/h) = < (w/s) < Gap Width, S (mils) Conclusions: The Lange Coupler linear model is an accurate design tool since its s- parameters show reasonable agreement with electromagnetic simulations. The linear model facilitates design studies due to its speed and ease of changing parameters. This allows parameter sweeps and performance optimization in the GENESYS enironment. Indiidual parameters can be changed and the resulting impact on the response can be obsered immediately. Using the Equation Block, the relationship between two ariables can be maintained as one is aried. To include coer effects and special geometries, the EM simulation is appropriate. C:\Desktop\Models_Lange\LANGE_note_01.doc

16 For more information about Agilent EEsof EDA, isit: Agilent Updates Get the latest information on the products and applications you select. Agilent Direct Quickly choose and use your test equipment solutions with confidence. For more information on Agilent Technologies products, applications or serices, please contact your local Agilent office. The complete list is aailable at: Americas Canada (877) Latin America United States (800) Asia Pacific Australia China Hong Kong India Japan 0120 (421) 345 Korea Malaysia Singapore Taiwan Thailand Europe & Middle East Austria Belgium 32 (0) Denmark Finland 358 (0) France * *0.125 /minute Germany ** **0.14 /minute Ireland Israel /544 Italy Netherlands 31 (0) Spain 34 (91) Sweden Switzerland United Kingdom 44 (0) Other European Countries: Reised: March 27, 2008 Product specifications and descriptions in this document subject to change without notice. Agilent Technologies, Inc. 2008