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RF Impedance Matching Using Stubs and Lumped Elements

Key Takeaways

  • RF impedance matching can be implemented in two different ways - 

a. Matching the source and load impedances  [ZS=ZL]

b. Matching the characteristic impedance with load impedance [ Z0=ZL]

  • Stub impedance matching utilizes transmission line segments called stubs. Based on the number of stubs used, the stub impedance matching can be bifurcated into single-stub matching and double-stub matching.

  • In monolithic integrated circuits, the lumped element passive components are employed for impedance matching.

 RadioFrequency ❲RF❳ranges from 20kHz to 300GHz

Figure 1: Electromagnetic wave spectrum 

It is a common practice in neural networks, artificial intelligence, machine learning, and statistics to generalize the input-output relationship by observing the same in certain learning sets. However, generalizing the electromagnetic signal propagation and behavior in this manner would be a bad idea. For instance, cent percent reflection of light signals is preferred for clear vision, whereas in RF engineering, any reflection of transmitted signals is taboo. If you want your RF system to be lossless, there should be no returning of RF signals from the output to input. 

The signal reflection in RF circuits is natural and unavoidable. The best method to make the circuit lossless is to incorporate impedance matching circuits. RF impedance matching circuits is a network of resistance (R ), inductance (L), and capacitance (C), carefully chosen and arranged to match the input impedance with output impedance. When the input impedance matches with output impedance, the RF circuit on which you are working goes to the genre of maximum power transfer, or zero loss circuits. 

RF impedance matching

The fundamental principle of RF impedance matching is to design and place an impedance network which removes any impedance mismatch present in the circuit. To be more clear, consider a simple RF circuit given in Figure 2, consisting of source and load connected via transmission lines. Let ZS and ZL be the source impedance and fixed load impedance, respectively. 

The thumb rule in impedance matching is to satisfy the conditions: either ZS=Zor Z=ZL, where Z0 is the characteristic impedance of the circuit. Incorporating an impedance matching network can aid in satisfying the above two conditions and thus attributes to a lossless RF circuit.

For impedance matching, conditions to be satisfied are either ZS=ZLor Z0=ZL

Figure 2:  Simple RF circuit

Just have a look at the internal PCBs in any radio, mobile phone, or computer WiFi card. You will find a lot of passive components and integrated circuits, indicating it's not simple RF circuits you are dealing with—impedance matching is much more complex than is often thought. 

Matching source and load impedance

In impedance matching, the source impedance matches the load impedance. The usual procedure is to terminate the circuit with the complex conjugate of the source impedance. If the source impedance is ZS= RS+jXS, the load impedance Zshould be RS-jXS for impedance matching. For achieving this condition, lumped or distributed impedance networks can be included in the circuit. The working frequency of the given circuit is significant in the design of the impedance matching circuits. 

Stub matching

Stub matching is the most elementary type of impedance matching network. The stubs are frequently used to match the complex load impedance to transmission line impedance. In stub matching, there are no passive elements involved. It is the parallel or series connection of transmission line segments called stubs, to the main transmission line at appropriate distances from the complex load impedance. The stubs can be open-ended or shorted. There are chances of radiation emissions from the open ends, so shorted stubs are of high demand.

Single-stub matching

 For single-stub impedance matching, satisfy Yin=Yl

Figure 3: Single-stub matching

As the name indicates, single-stub matching utilizes a single stub and transmission line, as shown in Figure 3, to satisfy the source and load impedance matching. Both open and short-circuited stubs are employed in this type of stub matching. However, the shorted stubs offer isolation in RF circuits, in which power supplies are present. 

For example, in RF amplifier circuits, the ends of the shorted-stubs are used to feed the bias voltages, and bypass the RF currents to the ground plane via a capacitor. The isolation between the power plane and ground plane is achieved through the short-circuited stubs. As illustrated in Figure 3, the transmission line length, l1, and stub length, l2, are adjusted in such a way that the load admittance, Yl, takes the desired value, Yin.

Double-stub matching

Figure 4 presents double-stub matching, where two stubs are used for impedance matching. Contrary to single-stub matching, impedance matching is achieved by only varying the length of stubs. The load impedance matching attained by keeping the transmission line length lconstant, enables the double-stub implementation useful in fixed-length tuners. The stub in the load side, l3, can be adjusted to fix the load admittance and further lfor successful impedance matching. 

 In double-stub impedance matching, transmission line length is kept constant

Figure 4: Double-stub matching

Impedance matching with lumped elements

In monolithic integrated circuits, there is no room for stub-impedance matching. The substrate space limitation calls for lumped elements for impedance matching in such ICs. Passive elements  L and C are arranged in various fashions to construct impedance matching circuits. Some are shown in Figure 5. The spiral inductors and metal-insulator-metal (MIM) capacitors suffice the inductance and capacitance requirements. 

Figures 5a and 5b correspond to low-pass networks, whereas 5c and 5d show high-pass networks. The lumped element passive component arrangement for a low-pass network differs from that of a high-pass network. The design topology of the lumped element impedance matching network is determined by factors such as attenuation, biasing, pass-band and stop-band frequency. 

Figure 5a and 5b shows low-pass networks

Figure 5: Lumped element impedance matching networks

Figure 5c and 5d presents high-pass networks

If you are planning to try RF impedance matching and your choice is lumped element matching networks, then it’s the time to access the Smith charts and software-based optimizations. You can easily set your sight on the appropriate arrangement of the L and C lumped components with Smith charts and the right software tool, in order to ensure zero reflection of RF signals.