# What's the S parameter in an Antenna

So, I'm struggling to understand what the S-parameter is in real-life terms; I mean, what does the S-parameter tell us about an antenna?

I have designed a microstrip Wi-Fi antenna that should work at around 2.4 GHz

I have simulated it and as the image below shows, the S-parameter seems correct to me with its down peaking at 2.4 GHz My problem is, practically speaking, what shows me the S-parameter?

I know that the parameter describes how voltages or currents behave in bi or quadripole but I can't understand how to mirror this theoretical description in my specific example with an antenna working on a certain frequency

## 2 Answers

S-parameters are a way of expressing things with general waves instead of voltages and currents. It describes how much the waves are reflected or transmitted from/through a device.

With a device like an antenna, there‘s not only 1 but 4 S-parameters. The first one S_11 is also known as the the reflection coefficient.

If an antenna is tuned and matched, it is obvious that S_11 should be as small as possible at the operating frequency. (No wave should be reflected when feeding the antenna)

Maybe you don‘t want your antenna to be tuned to 2.4GHz, but to 2.44GHz, because with most radios like ZigBee or Bluetooth, you want to tune the antenna to the center of the frequency band.

The graph shows (negative) return loss ($$\RL\$$) and, for the relevant s-parameter ($$\S_{11}\$$) the relationship is: -

$$RL = -20\log_{10}|S_{11}|$$

So, at the lowest point on the graph (-17 dB), $$\|S_{11}|\$$ = 0.1413.

$$\S_{11}\$$ is also called the reflection coefficient ($$\Γ\$$).

And, the reflection coefficient ($$\Γ\$$) also equals: -

$$Γ = \dfrac{Z_L - Z_S}{Z_L + Z_S}$$

Rearranging the above gives us: -

$$Z_L = Z_S\cdot\dfrac{1+Γ}{1-Γ}$$

My problem is, practically speaking, what shows me the S-parameter?

So, if $$\Z_S\$$ is 50 ohms and $$\|S_{11}|\$$ is 0.1413, $$\Z_L\$$ = 66.5 ohms....

However, because we only know the magnitude of $$\S_{11}\$$, $$\Z_L\$$ could be 37.6 ohms as per the inverse of the above equation: -

$$Z_L = Z_S\cdot\dfrac{1-Γ}{1+Γ}$$

Return loss and reflection coefficient calculator