Let’s Talk About Impedance Matching​

Let’s Talk About Impedance Matching​

Acousto-Optic Effect & Acousto-Optic Devices​​

When ultrasonic waves propagate through a medium, they generate elastic strains that vary periodically in time and space, creating alternating regions of compression and rarefaction—analogous to a phase grating. When light passes through a medium perturbed by ultrasonic waves, diffraction occurs. This phenomenon is known as the acousto-optic effect. Devices developed based on this effect are called acousto-optic (AO) devices.

A typical acousto-optic device consists of three main components:

①​​Ultrasonic transducer​​; ②​​Acousto-optic medium​​； ③​​Matching network​​

As shown in Figure 1:

Figure 1. Structure of a Typical Acousto-Optic Device​​

Matching Network & Impedance Matching​​

The matching network consists of components such as capacitor, inductor, RF cable, and connector. Such networks are utilized not only in acousto-optic devices but also in systems like high-frequency wired networks, radar, and fiber-optic communications. Impedance matching is not only a critical part of acousto-optic devices but also an indispensable component of high-frequency communication devices. It is essential for achieving lossless transmission.

So, what is impedance? And what exactly is impedance matching? This class will explain these concepts in detail.

Resistance & Impedance​​

① Resistance​​

Resistance refers to the part of an electrical circuit that opposes the flow of electric current and dissipates energy. Examples include resistors in circuits and heating elements in electric blankets, which convert electrical energy into heat.

Figure 2. Various Types of Resistors (Image Source: Internet)​​

Impedance​​

Impedance is a fundamental concept that can be simplified as resistance or extended to characterize characteristic impedance. By definition, impedance is the instantaneous voltage divided by current, which resembles the definition of resistance. The key difference is that impedance includes not only resistive components but also capacitive and inductive elements.

Interesting Fact​

Why do many RF systems or components use a characteristic impedance of 50Ω, rather than 60Ω or 70Ω? How was this value determined, and what is the rationale behind it?

In 1929, Bell Laboratories conducted extensive experiments and found that coaxial cables with characteristic impedances of 30 Ω and 77 Ω optimally balanced high-power transmission and low loss. Specifically:​​30 Ω coaxial cables​​ maximize power transmission capacity. ​​77 Ω coaxial cables​​ minimize signal loss. The arithmetic mean of 30Ω and 77 Ω is 53.5 Ω, while their geometric mean is 48 Ω. The widely adopted 50 Ω system impedance represents an engineering compromise between these two values, aiming to simultaneously achieve high power transmission and low loss. Moreover, practical applications have demonstrated that a 50 Ω system impedance effectively matches the port impedance of half-wave dipole antennas and quarter-wave monopole antennas, minimizing reflective losses.

Impedance Matching​​

Impedance matching is a fundamental concept in microwave electronics, primarily applied to transmission lines to ensure that all high-frequency microwave signals are efficiently delivered to the load point [1].

Figure 3. Schematic Diagram of Ideal Impedance Matching (Image Source: Internet)​​

However, in practical scenarios, the source impedance is typically not 50 Ω, nor is the load impedance. This necessitates the implementation of impedance matching circuits.

Figure 4: Impedance Mismatch vs. Match (Image Source: Internet)​​

In low-frequency circuits, transmission line matching is generally not a concern, and focus remains primarily on the interaction between the signal source and the load. However, in high-frequency circuits, reflection effects must be considered. When the signal frequency is sufficiently high such that the wavelength becomes comparable to the length of the transmission line, the reflected signal superimposes onto the original signal, distorting its waveform.

If the characteristic impedance of the transmission line does not match the load impedance, reflections occur at the load end. To prevent such reflections, the load impedance must equal the characteristic impedance of the transmission line—this is the principle of impedance matching in transmission lines. Typically, impedance matching involves the following three scenarios:

Case 1: As shown in Figure 5, when impedance is well-matched, signals propagate smoothly through the system without obstruction, enabling lossless energy transmission.

Figure 5. Well-Matched Impedance

Case 2: As illustrated in Figure 6, the presence of impedance mismatch nodes causes reflective loss of transmitted signal energy. Consequently, the energy received by the subsequent stage is less than the output energy from the preceding stage.

Figure 6. Poorly Matched Impedance

Case 3: As depicted in Figure 7, under complete impedance mismatch, the energy of the transmitted signal fails to transfer from the preceding matching stage to the subsequent stage. Instead, the energy is entirely reflected back to the preceding stage, resulting in complete system failure.

Figure 7. Complete Impedance Mismatch

Methods and Types of Impedance Matching​​

Taking acousto-optic devices as an example, impedance matching circuits are typically implemented using three configurations: L-type, π-type, and T-type networks [2-4].

L-Type Matching​​

As shown in Figure 8, this circuit offers simplicity and low cost but is limited to narrowband applications. L-type matching requires careful consideration of matching efficiency and power loss, ideally utilizing inductive and capacitive components. There are eight fundamental circuit variations available for selection [5].

Figure 8. Eight Configurations of L-Type Matching (Image Source: Internet)

For example, in our company’s acousto-optic devices, the initial impedance without a matching circuit deviates significantly from the standard 50Ω (see Figure 9).

Figure 9. Initial Impedance of the Acousto-Optic Device

If driven directly by an RF signal under such conditions, excessive reflection would occur, potentially damaging the RF source. After applying L-type matching, the impedance is effectively tuned to approximately 50Ω (see Figure 10).

Figure 10. Impedance After L-Type Matching

Figure 11. Bandwidth After L-Type Matching

T-Type and π-Type Circuits​​

As illustrated in Figures 12 and 13, these configurations allow adjustment of the circuit’s quality factor (Q factor), offering greater flexibility. Multi-component matching networks can reduce the Q factor while broadening the bandwidth[6-7].

Figure 12. T-Type Matching Circuit

Figure 13. π-Type Matching Circuit

Figure 14. shows the standing wave pattern after π-type circuit matching, demonstrating a significant increase in device bandwidth post-matching.

Figure 14. Bandwidth of Acousto-Optic Device After π-Type Matching

Summary​​

Whether designing lumped-parameter circuits or microwave circuits, it is essential to recognize the following principles:

To increase impedance, use a series configuration.

To decrease impedance, use a shunt configuration.

The L-type matching circuit is the simplest design and is often the preferred choice for lower-frequency applications [8]. If quality factor (Q) control is required, T-type or π-type matching circuits should be considered.Matching circuit design is not a standalone process; it requires comprehensive consideration of interactions with bias circuits, feedback networks, and frequency tuning circuits. Iterative design and modifications are often necessary to achieve satisfactory results [9].

Impedance matching technology finds applications in RF circuits, acoustic systems, optical systems, and mechanical systems. Understanding impedance matching enables the selection of optimal matching strategies to enhance performance in high-frequency signal transmission.

In conclusion, impedance matching is a critical aspect of the manufacturing and application of acousto-optic devices. Even minor disruptions, such as physical contact or displacement of internal components during assembly or use, may cause impedance mismatch, leading to performance degradation or device failure. Therefore, careful handling during assembly is imperative. Should any mismatch issues arise, please do not hesitate to contact our technical support team.

References​

[1] Reinhold Ludwig, Pavel Bretchko. RF Circuit Design: Theory and Applications[M]. Beijing: Publishing House of Electronics Industry, 2002, pp. 270-305.

[2] Reich M T, Bauer-Reich C. UHF RFID Impedance Matching: When Is a T-Match[J]. IEEE International Conference on RFID, 2014, pp. 24-30.

[3] Chung B K. Q-Based Design Method for T-Network Impedance Matching[J]. Microelectronics Journal, 2006, 37(9): 1007-1011.

[4] Chung B H K, Lin Y S, Lu S S. Analysis and Design of a 1.6–28 GHz Compact Wideband LNA in 90 nm CMOS Using a π-Matching Input Network[J]. IEEE Transactions on Microwave Theory and Techniques, 2010, 58(8): 2092-2104.

[5] Mattaei G L. Microwave Filters, Impedance-Matching Networks, and Coupling Structures[M]. Reprinted by Artech House, 1980. (Note: Original citation adjusted to standard format.)

[6] Liao Chengen. Fundamentals of Microwave Technology[M]. Beijing: Posts & Telecom Press, 1998.

[7] Zhao Chunhui, Zhang Chaozhu. Microwave Technology[M]. Beijing: Higher Education Press, 2007, pp. 40-47.

[8] Wen Yingchun. Application of Impedance Matching Circuits in Filter Testing[J]. Electronic Science and Technology, 2012, 25(7): 90-91.

[9] Tian Yapeng, Zhang Changmin, Zhong Weiwei. Principles and Applications of Impedance Matching Circuits[J]. Electronic Science and Technology, 2012, 25(1): 6-7.