Why Impedance Matching Is Necessary

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Estimated reading time: 15 minutes

The biggest difference between radio frequency (RF) and hardware lies in impedance matching, and the reason for impedance matching is the transmission of electromagnetic fields. As we all know, an electromagnetic field is the interaction between an electric field and a magnetic field. The loss in the transmission medium occurs because the electric field causes oscillations in its effect on electrons. The higher the frequency, the more cycles of electromagnetic waves there are in a transmission line of the same length, and the higher the frequency of current changes. As a result, the heat loss generated by oscillations increases, leading to greater losses in the transmission line.

At low frequencies, since the wavelength is much longer than the transmission line, the voltage and current on the transmission line in the circuit remain almost unchanged, so the transmission line loss is very small.

Meanwhile, if reflection occurs during wave output, the superposition of the reflected wave with the original input wave may lead to a decline in signal quality and also reduce the efficiency of signal transmission.

Whether working on hardware or RF systems, the goal is to achieve better signal transmission, and no one wants energy to be lost in the circuit.

When the load resistance is equal to the internal resistance of the signal source, the load can obtain the maximum output power. This is what we often refer to as impedance matching. 

It is important to note that conjugate matching is for maximum power transmission. 

According to the voltage reflection coefficient formula \( \Gamma = \frac{Z_L - Z_0}{Z_L + Z_0} \), \( \Gamma \) is not equal to 0 at this time, meaning there is voltage reflection. 

For distortionless matching, the impedances are completely equal, so there is no voltage reflection. However, the load power is not maximized in this case.

Return Loss (RL) = \( -20\log|\Gamma| \)

Voltage Standing Wave Ratio (VSWR) = \( \frac{1 + |\Gamma|}{1 - |\Gamma|} \)

The relationship between standing wave ratio and transmission efficiency is shown in the table below: 

Impedance matching involves a rather tedious calculation process. Fortunately, we have the Smith Chart, an essential tool for impedance matching. The Smith Chart is a diagram composed of many intersecting circles. When used correctly, it allows us to obtain the matching impedance of a seemingly complex system without any calculations. The only thing we need to do is read and track data along the circular lines. 

## Smith Chart Method 

1. After connecting a series capacitor component, the impedance point moves counterclockwise along the constant-resistance circle it is on. 

2. After connecting a shunt capacitor component, the impedance point moves clockwise along the constant-conductance circle it is on. 

3. After connecting a series inductor component, the impedance point moves clockwise along the constant-resistance circle it is on. 

4. After connecting a shunt inductor component, the impedance point moves counterclockwise along the constant-conductance circle it is on. 

5. After connecting a shunt open-stub component, the impedance point moves clockwise along the constant-conductance circle it is on. 

6. After connecting a shunt short-stub component, the impedance point moves counterclockwise along the constant-conductance circle it is on. 

7. After connecting a series transmission line component, the impedance point moves clockwise along the constant-standing-wave circle.

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