![]() ![]() That resonant equivalent resistance (R R) of a parallel RLC circuit can be calculated by: Recall that a parallel resonant circuit acts like an equivalent resistance. ![]() In this example, the capacitor, inductor, and load resistance form a parallel resonant circuit (Fig. Match the output impedance of 50 Ω from a 433-MHz industrial-scientific-medical (ISM) band transmitter to a 5-Ω loop antenna impedance (Fig. If the Q is greater than 5, you can use the simplified approximations: These equivalents also can help explain how the L-networks and other impedance-matching circuits work. Such conversions are useful in RLC circuit analysis and design (Fig. Sometimes it’s necessary to convert a series RC or RL circuit into an equivalent parallel RC or RL circuit or vice versa. Also the series equivalent load of 10 Ω matches the generator resistance for maximum power transfer. Note how the series equivalent capacitive reactance equals and cancels the series inductive reactance. You can see how this matching network functions by converting the parallel combination of the 50-Ω resistive load and the 25-Ω capacitive reactance into its series equivalent (Fig. The bandwidth (BW) of the circuit is relatively wide given the low Q of 2:īW = f/Q = 76 x 10 6/2 = 38 x 10 6 = 38 MHz When these factors are known, the computed values can be compensated. This solution omits any output impedance reactance such as transistor amplifier output capacitance or inductance and any load reactance that could be shunt capacitance or series inductance. Calculate the needed inductor and capacitor values using the formulas given in Figure 1a: Assume an amplifier output (generator) impedance of 10 Ω at a frequency of 76 MHz. Most power amplifiers have a low output impedance, typically less than 50 Ω. The goal is to match the output impedance of a low-power RF transistor amplifier to a 50-output load, and 50 Ω is a universal standard for most receiver, transmitter, and RF circuits. This problem can sometimes be overcome by switching from a low-pass version to a high-pass version or vice versa. In some instances, the calculated values of inductance or capacitance may be too large or small to be practical for a given frequency range. There are limits to the range of impedances that it can match. While the L-network is very versatile, it may not fit every need. These choices will be covered in a subsequent article. If it is essential to control Q and bandwidth, a T or p-network is a better choice. The impedances that are being matched determine the Q of the circuit, which cannot be specified or controlled. The key design criteria are the magnitudes and relative sizes of the driving generator output impedance and load impedance. The low-pass versions are probably the most widely used since they attenuate harmonics, noise, and other undesired signals, as is usually necessary in RF designs. There are four basic versions of the L-network, with two low-pass versions and two high-pass versions (Fig. Any RF circuit application covering a narrow frequency range is a candidate for an L-network. Another use is matching an antenna impedance to a transmitter output or a receiver input. L-networks are useful in matching one amplifier output to the input of a following stage. The primary applications of L-networks involve impedance matching in RF circuits, transmitters, and receivers. L-Network Applications And Configurations This article will introduce the L-network, which is a simple inductor-capacitor (LC) circuit that can be used to match a wide range of impedances in RF circuits. “ Back to Basics: Impedance Matching (Part 1)” discusses the use of a transformer as a basic way to match impedance. The need arises in virtually all electronic circuits, especially in RF circuit design. This article is part of the Analog Series: Back to Basics: Impedance Matchingĭuring impedance matching, a specific electronic load (R L) is made to match a generator output impedance (R g) for maximum power transfer. ![]()
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