### 4. Know the difference between return loss and reflection coefficient

There are two S-parameters of interest in a 2-port device. The first is the reflection coefficient, S11, that measures the ratio of the reflection from Port 1 to the drive signal at that port. The second is the transmission coefficient, S21, that is the ratio of the output of Port 2 to the drive signal into Port 1. Confusion arises because historical measurements of return loss and insertion loss are often used interchangeably with reflection coefficient and transmission coefficient, respectively.

The source of this confusion is the method used to make this measurement before the availability of vector network analyzers (VNAs). Return loss was measured by driving a signal source into an open circuit and measuring the reflected signal. Of course, since 100% of the signal was reflected back to the source by the open, this was used as a reference power level. Next, the device under test was inserted and the test repeated (Figure 2). Return loss was calculated using the ratio of power reflected from the open (the reference level) compared to the power reflected from the input port with the DUT connected:

*Return Loss*= 10 *

*Log*((

*P reference)*/(

*P reflected*))

Figure 2. Return loss is measured by comparing power reflected from the DUT with power reflected from an open circuit. Return loss will always be a positive, scalar value. |

The return loss in dB is -1 times the magnitude of the reflection coefficient S11.

The smaller the S11 magnitude, the greater the return loss and vice versa. So, the better the impedance match at Port 1, the greater the return loss and the smaller S11, the reflection coefficient.

You will hear S11 referred to as the “return loss”, but when you hear S11, you should always think “reflection coefficient” to avoid confusion.

### 5. Know the difference between insertion loss and transmission coefficient

Figure 3. Insertion loss measures the power at Port 2 without the DUT and then with the DUT inserted. |

Insertion loss is then the loss in the signal due to insertion of the DUT.

*Insertion Loss*= 10 *

*Log*((

*P witout DUT )*/(

*P with DUT*))

When you hear “insertion loss”, think “S21 transmission coefficient is -1* insertion loss in dB”.

### 6. Know S-parameters are ratios of voltages described as ratios of power (dB)

When we look at S-parameters, we calculate them as the ratios of voltages. If they are expressed in dB, we have to be a little careful because dB is basically a ratio of measured powers.We have to look at the underlying voltage associated with that power. Power is related to the square of the voltage resulting in the following:*A_dB*= 10 *

*Log P_Out*/

*P_In*= 10 *

*Log (V_Out)*^2/(

*V_In)*^2 = 20 *

*Log V_Out*/

*V_In*

Note that when we compute dB with voltages, there is a factor of 2 that accounts for the squaring of the voltage measurements to convert them to power. In converting from dB to voltage ratios, the factor of 20 must be used:

*V_Out*/

*V_In*= 10^(

*A_dB*/20)

Using these equations, we can compute some significant voltage dB ratios:

**Ratio of Voltage**

**Amplitudes (%)**

**Value in dB**100 0

90 -1

80 -2

70 -3

50 -6

30 -10

10 -20

5 -26

3 -30

1 -40

__Let’s take a look at a simple example of S-parameter measurements comparing two different connectors (Figure 4). The K connector has a rated bandwidth of 40 GHz, while the SMA connector’s bandwidth is 18 GHz. The transmission coefficient of the K connector is near 0 dB, while that of the SMA connector drops below 0 dB, to about -3 dB, between 20 and 32 GHz. Remember that the insertion loss is -1 times the transmission coefficient, so that the maximum insertion loss of the SMA connector is about 3 dB. At that frequency, only about 70% of the applied voltage is reaching the output port.__

Likewise, the reflection coefficient of the SMA at around 25 GHz is -4 dB. This means that the return loss is 4 dB.

For a more in-depth and up-to-date treatment of this topic, watch Dr. Eric Bogatin's webinar series on High-speed Interconnect Characterization.

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