A method of measuring reflection coefficient

Abstract

A circuit for measuring the reflection coefficient and a method for testing and calibration are proposed. The measurement circuit consists of two cascaded orthogonal directional couplers, with the through-terminal and coupling terminals of the two couplers connected to the same reactive element. Measuring the voltage between the through-terminal and coupling terminals under short-circuit conditions allows for calibration of the reflection coefficient of the reactive element. Based on the measured voltages between the through-terminal and coupling terminals of the two orthogonal directional couplers, a system of two nonlinear equations can be constructed. Solving this system yields the real and imaginary parts of the reflection coefficient of the load under test.

Description

Technical Field

[0001] This invention relates to microwave measurement technology. Background Technology

[0002] Methods for measuring reflection coefficient can be divided into two categories: coherent detection and incoherent detection. Most commercial measuring instruments are based on coherent detection, which requires measuring the in-phase and quadrature components of a complex signal. This method offers a large dynamic range and low noise level, but the circuitry is complex, the cost is high, and the measuring equipment is relatively large. Reflection coefficient measurement based on incoherent detection typically estimates the amplitude and phase of the signal under test through power measurement. Its circuitry is relatively simple and the cost is lower. It has application value in some sensing and field monitoring measurement applications.

[0003] Traditional non-correlated detection methods require the use of measurement line probes to extract voltage information at various points on the transmission line when measuring power, but the analysis, design, and manufacturing of these probes are complex. This invention proposes a non-coherent detection circuit for the reflection coefficient. This method extracts relevant information by measuring the voltage between the through-end and coupled reactive components of an orthogonal directional coupler. It causes minimal interference to the system under test and is easy to implement. It can be used for near-field non-destructive testing, material characterization, etc. Summary of the Invention

[0004] When the through-end and coupled-end of an orthogonal directional coupler are terminated with the same reactive element, its input and isolation ends can be considered as a phase shifter, and its scattering parameter matrix is ​​the same as the transmission line matrix. Thus, changing the reactive loads terminated at the through-end and coupled-end can simulate transmission lines of different electrical lengths. Furthermore, the voltage across the reactive elements at both ends is a function of the reflection coefficient of the load under test. Therefore, it is possible to measure the reflection coefficient of the load under test by measuring the voltage across the reactive elements at both ends. Figure 1 The orthogonal directional coupler shown has 1 as the input terminal, 2 as the through terminal, 3 as the coupling terminal, and 4 as the isolation terminal. Its scattering parameters satisfy the following relationship.

[0005] here k The coupling coefficient is the coefficient when the directional coupler is lossless.

[0006]

[0007] This results in an ideal 3 dB orthogonal directional coupler. In this design, only amplitude balance between the 2-port and 3-port is required, and k can be less than or equal to 0.707.

[0008] Figure 1The through-end and coupling end of the orthogonal directional coupler shown are connected to the same component, and its reflection coefficient is Γ. A You can get

[0009] Figure 2 This is a circuit for measuring the reflection coefficient, where A and B are 3 dB orthogonal directional couplers. The port definitions here are the same as... Figure 1 The following configurations are identical: 1 is the input terminal, 2 is the through terminal, 3 is the coupling terminal, and 4 is the isolation terminal. The through and coupling terminals of each coupler are connected to a reactive element with a reflection coefficient of ΓA. Port 4 of coupler A is connected to a reactive element with a reflection coefficient of ΓA. Γ L The load under test is connected to a signal source at port 1 of coupler B. For ease of derivation, the following assumes the coupling coefficient of the coupler is... k It equals 0.707.

[0010] For coupler A, the reflected wave at its 3-port can be expressed as:

[0011] Based on the properties of orthogonal directional couplers, S 33 =0, S 32 =0, therefore we have

[0012] because

[0013] In addition, we can obtain from equation (3)

[0014] Substituting (6) and (7) into (5), we can obtain

[0015] If let

[0016]

[0017] It can be obtained

[0018] Similarly, for port 2 of coupler A, its reflected wave can be expressed as...

[0019] A similar derivation can be obtained

[0020]

[0021] Using equations (9) and (12), we can obtain

[0022] For coupler B, its 4-port equivalent load reflection coefficient is:

[0023] By performing a similar analysis to that of coupler A, we can obtain...

[0024] When Γ L =-1, from equation (13) we have

[0025] Assuming that terminals 2 and 3 of the coupler are connected to the same capacitive element, if we let

[0026] The value of θ should be within the interval [-π, 0]. This can be obtained...

[0027] Formula (17) can be used to determine the reflection coefficient Γ of the reactive element by means of a short-circuit calibration measurement at the terminal. A .

[0028] After determining θ through load short-circuit calibration measurement, the reflection coefficient of the load under test can be determined by measuring the voltage at terminals 2 and 3 of each coupler. Let the reflection coefficient of the load under test be Γ. L =x+jy.

[0029] The voltage amplitude V at terminals 2 of coupler A was measured. 2A The voltage amplitude V at terminals 3 of coupler A 3A From equation (13), we can obtain

[0030] Measure the voltage amplitude V at terminals 2 of coupler B. 2B With the voltage amplitude V at terminal 3 3B From equation (15), we can obtain

[0031] Simplify and rearrange to obtain

[0032]

[0033] Treating equations (20) and (21) as a system of two nonlinear equations, the constraints on the unknowns x and y are as follows:

[0034] By performing nonlinear optimization, we can obtain x and y, and determine Γ. L . Attached Figure Description Figure 1 A directional coupler in which the coupling end and the through end are connected to the same reactive element.

[0035] Figure 2 For measurement circuits. Detailed Implementation

[0036] (1) Measurement circuit connection: such as Figure 2 The circuit shown is connected to the reflection coefficient measurement circuit, where A and B are 3 dB orthogonal directional couplers. The port definitions here are the same as... Figure 1 The terminals are identical: 1 is the input terminal, 2 is the through terminal, 3 is the coupling terminal, and 4 is the isolation terminal. The through and coupling terminals of each coupler are both connected to a reactive element with a reflection coefficient of ΓA. Terminal 4 of coupler A is connected to the load under test, and terminal 1 of coupler B is connected to the signal source.

[0037] (2) Calibration: Calibration is performed before measurement: Short-circuit terminals 4 of coupler A, measure the voltage between terminals 3 and 2 of coupler A, and calculate Γ using formula (17). A .

[0038] (3) Test: During measurement, connect the load to be tested to terminal 4 of coupler A and measure the voltage V at terminal 3 of coupler A. 3A With the voltage V at both ends 2A Measure the voltage V at terminals 3 of coupler B. 3B With the voltage V at both ends 2B Then, the reflection coefficient Γ of the load under test is obtained by solving formulas (18), (19), (20), and (21). L .

Claims

1. A single-port network reflection coefficient measurement circuit: consisting of two identical orthogonal directional couplers A and B cascaded together, with coupling port 3 of coupler A connected to through port 2, and a reflection coefficient of Γ. A The reactive phase-shifting load, the coupling port 3 of coupler B is connected to the through port 2, and the reflection coefficient is Γ. A The reactance phase-shifting load; the isolation port 4 of coupler A is connected to the load under test, the input port 1 of coupler 1 is connected to the signal source, and the input port 1 of coupler A is directly connected to the isolation port 4 of coupler B.

2. A calibration method for the single-port network reflection coefficient measurement circuit of claim 1: short-circuit the isolation port 4 of coupler A, and measure the voltage amplitude V at port 2 of coupler A. 2A The voltage amplitude V at the 3-port of coupler A 3A The phase-shifting reactance load Γ connected to ports 2 and 3 of coupler A is solved using the following formula. A Argument θ: 。 3. A measurement method for the single-port reflection coefficient measurement circuit of claim 1: The load to be measured is connected to the 4 ports of coupler A; the amplitude ratio P1 of the voltage at port 3 to the voltage at port 2 of coupler A is measured; the amplitude ratio Q1 of the voltage at port 3 to the voltage at port 2 of coupler B is measured; and the real part x and the imaginary part y of the reflection coefficient are solved using the following nonlinear equations: 。

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