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Transmission Line Designer >
Transmission Lines >
Lange Coupler

Lange Coupler

Keyword	Default	Unit	Description
N	Req (Phys)	m	Number of strips (2, 4, or 6)
W	Req (Phys)	m	Spacing between conductors
S	Req (Phys)	m	Spacing between strips
Sps	10		Number of substrips used in the analysis. Substrips/strip × number of strips ≤ 60
Z	50	ohm	Connecting line impedance to account for impedance change from feed line to coupler
P	Req (Elec Opt 2)	m	Physical length of the coupler
K	Req (Elec Opt 1)	dB	Coupling coefficient (positive)
Z0	Req (Elec Opt 1)	ohm	Impedance of the coupled lines
Ze	Req (Elec Opt 2)	ohm	Even-mode impedance of the coupled lines
Zo	Req (Elec Opt 2)	ohm	Odd-mode impedance of the coupled lines
E	0	deg	Electrical length of the coupler
Frequency	0	Hz	The frequency at which the quasistatic calculations are performed and reused at other analysis frequencies
H	Required	m	Substrate thickness
Er	Required		Relative dielectric constant
Thickness	0	m	Thickness of metallization
TAND	0		Dielectric loss tangent
Bond Wire Number	Required when activated		Number of bond wires used to connect the interdigital strips

Keyword	Default	Unit	Description
Bond Wire Diameter	Required when activated	m	Diameter of bond wires
Bond Wire Spacing	Required when activated	m	Spacing between bond wire centers
Line Disc. Width	Required when activated	m	Width of the connecting line to account for the impedance discontinuity in the calculations

Synthesis and Analysis

Synthesis of a Lange coupler proceeds by first selecting the number of strips for the desired structure. Two options exist for synthesis:

— Specify impedance, Z0, and the coupling coefficient, K.

— Specify the even-mode impedance, Ze, and the odd-mode impedance, Zo.

• The substrate parameters H, and ER must be entered prior to clicking the Synthesis button. The width of the strips, Width, and the spacing between them, Spacing, will be computed. Also, the alternate electrical option set will be computed (e.g., if Z0 and K are entered, Ze and Zo will be computed).

• For analysis, the parameters Width, Spacing, H, ER and either Physical Length or Frequency must be entered prior to clicking the Analysis button. The electrical properties, Z0, K, Zo, and Ze will be computed.

• Conversion from electrical length, E, to physical length, P, can be performed by entering a value for E and the frequency, Frequency. Click Synthesis to compute P. Similarly, to convert from physical length to electrical length, enter values for P and Frequency and click Analysis to compute E.

Dielectric Substrates

A dielectric substrate is defined by the parameters H, ER, and TAND. The substrate is assumed to be lossless unless TAND is specified and greater than zero.

Conductor Metallization

The default conductor used for analysis is gold whose resistivity is 2.44 mohm-cm. The thickness of the metal can be specified using the Thick parameter in the substrate group. The calculation uses the thickness for loss and impedance calculations.

Frequency Sweep Options

A frequency sweep can be performed to determine the response of the coupler over frequency. Type Start Stop Step (e.g., 4 6 5) and click Analysis.

Example

To select the Lange coupler, select TRL on the Product menu, click Microstrip, and click Lange Coupler. Set the units to mil and GHz. We will use the following parameters for synthesizing a 4 strip, 3-dB coupler at 10 GHz:

Number of Strips, N:	4
Impedance, Z0:	50 ohms
Coupling, K:	3 dB
Center Frequency:	10 GHz
Substrate thickness, H:	25 mil
Dielectric constant, ER:	10
Metal Thickness, Thick:	0.2 mil

Click the Synthesis button to determine the coupled line parameters:

Width, W	1.6545 mil
Spacing, S	2.0000 mil
Odd-mode impedance, Zo:	20.68 ohms
Even-mode impedance, Ze:	120.91 ohms

***** LANGE SYNTHESIS *****

COUPLING IMPEDANCES (OHMS) SUBSTRATE FULL STRIPS

DB EVEN ODD COUPLER ER H(mils) NO. T(mils) W(mils) S(mils)

3.00 120.91 20.68 50.00 10.00 25.0000 4 0.20000 1.6545 2.0000

To include the effects of a bond wire and connecting line parasitics, enter the following:

Bond Wire	Yes
Number	3
Diameter	.8 mil
Spacing	2 mil
Line Discontinuity	Yes
Width	24.5 mil

Clicking Analysis yields the following:

***** LANGE ANALYSIS *****

SUBSTRATE:

THICKNESS = 25.0000 mils

DIELECTRIC CONSTANT = 10.0000

LOSS TANGENT = 0.00000

STRIPS:

NUMBER = 4

WIDTH = 1.6545 mils

SPACING = 2.0000 mils

THICKNESS = 0.2000 mils

SUBSTRIPS = 10

PARASITICS:

NO. PARALLEL WIRES = 3

BOND WIRE DIAMETER = 0.8000 mils

WIRE SEPARATION = 2.0000 mils

WIDTH OF 50 OHM LINE = 24.5000 mils

W/H =0.066181 S/H =0.079999

W/H =0.071646 S/H =0.074534 EFFECTIVE VALUES DUE TO FINITE THICKNESS

*** DC CHARACTERISTICS

Z(0) = 50.00 Ohms

ZOE OHMS ZOO OHMS COUP DB Z(0) EFFKE EFFKO VE M/SEC VO M/SEC

131.56 22.81 3.04 54.79 6.378 5.502 1.1870E+8 1.2781E+8

*** CHARACTERISTICS WITH DISPERSION

CENTER FREQUENCY = 10000.0 MHZ

ZOE OHMS ZOO OHMS COUP DB Z(0) EFFKE EFFKO VE M/SEC VO M/SEC

134.08 23.18 3.03 55.75 6.380 5.510 1.1869E+8 1.2771E+8

EVEN MODE ATTENUATION ODD MODE ATTENUATION

db/in db/in

0.6087 2.1903 DIELECTRIC + CONDUCTOR

EFFECTIVE DIELECTRIC CONSTANT OF COUPLER = 5.9371

ESTIMATED COUPLING LENGTH = 121.098 mils

INDUCTANCE PER CROSSOVER LOCATION = 0.12526 nH

RESISTANCE PER CROSSOVER LOCATION = 0.04920 Ohms

*** RESPONSE WITH DISPERSION AND PARASITICS

FREQ. REFL. VSWR RET LOSS COUPL. PHASE THRU LOSS PHASE ISOLAT

(MHz) COEFF (dB) (dB) (Deg) (dB) (Deg) (dB)

10000 0.068 1.15 -23.3 3.23 -0.6 -3.11 -90.2 -24.66

DUE TO PARASITICS, THE CENTER FREQUENCY HAS SHIFTED DOWN FROM 10000 MHZ

To perform a frequency analysis from 4 GHz to 12 GHz in steps of 1 GHz, type 4 12 1 in the Frequency box. Then add coupling length P = 121.098 mil. The last part of the output will contain the analysis at each frequency. The 10 GHz center frequency analysis point is used to compute the quasistatic characteristics and reused at each analysis frequency.

FREQUENCY ANALYSIS OF COUPLER

FREQ. REFL. VSWR RET LOSS COUPL. PHASE THRU LOSS PHASE ISOLAT

(MHz) COEFF (dB) (dB) (Deg) (dB) (Deg) (dB)

4000 0.078 1.17 -22.1 5.99 42.2 -1.56 -45.6 -23.92

5000 0.081 1.18 -21.8 4.89 33.7 -2.02 -54.5 -23.42

6000 0.081 1.18 -21.8 4.17 26.0 -2.42 -62.5 -23.30

7000 0.079 1.17 -22.1 3.70 18.9 -2.74 -69.9 -23.41

8000 0.076 1.16 -22.4 3.41 12.2 -2.97 -76.9 -23.69

9000 0.072 1.16 -22.8 3.26 5.7 -3.10 -83.6 -24.11

10000 0.068 1.15 -23.3 3.23 -0.6 -3.11 -90.2 -24.66

11000 0.065 1.14 -23.8 3.33 -7.1 -3.02 -96.9 -25.34

12000 0.060 1.13 -24.4 3.56 -13.8 -2.81 -103.8 -26.03

Electrical Length [Eeff=(Effo+Effe)/2] = 35.78 deg

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