# s11 ( reflection coefficient ) to impedance conversion for simulation

s11 is the input reflection coefficient expressed in terms of s – parameters. It can be used as is in certain software programs to analyze the input characteristics of a 2 – port circuit. However, if these specialized programs are not available then a conversion between s11 can be carried out from the known ( measured) value of s11 using either the Smith Chart or by using a simple calculator for the conversion. The basic conversion algorithm is as follows:

Z = Zo * ((1 + Γ) / (1 – Γ))
Γ = (Z – Zo) / (Z + Zo)
S11 = 20 * Log10(mag)

Here Z is the impedance corresponding to the reflection coefficient, Zo is the characteristic impedance,  Γ is the reflection coefficient. Obviously the calculations involve complex numbers as the impedances and the reflection coefficient are all complex numbers. Another way to do the conversion is to use the Smith Chart. As shown below. Just input the value of s11 or the reflection coefficient and read the impedance at that point..The example below converts a s11 magnitude of 0.6966 and angle 176.2 to an equivalent impedance directly.

The Smith Chart program used here is a freeware program developed by Prof. Fritz Dellsperger , Juerg Tschirren and Roger Wetzel of the Berne Institute of Engineering and Architecture.

The same function can be done using a calculator as mentioned above. The results of the calculator are shown below:

The calculator used for this function was from Le Leivre.com on the web. Please visit the Signal Processing Group Inc., website for more technical information, white papers, and general information for our cost – effective design, development and manufacturing services for Analog and RF/wireless ASICs and modules.

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#### A wideand RF detector ( 40 Mhz to 3 Ghz) -75 dBm to 5 dBm input

A wideband RF detector

#### Linear detector performance

Linear detector performance curves

#### A wideband linear RF detector

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#### 2 stage amplifier deta

Please see details at http://www.signalpro.biz/2rf_amplifier_details.htm    Delivery lead time is 3 days. Return within 30 days for a full refund. Price is \$15.00 for one unit and \$10.00 per unit in volumes of 100. For higher volumes than 100 please contact Signal Processing group Inc.

#### Mni LNA performance

Delivery lead time is 3 days. Return within 30 days for a full refund. Price is \$15.00 for one unit and \$12.00 per unit in volumes of 100. For higher volumes than 100 please contact Signal Processing Group Inc. at email: spg@signalpro.biz or call 602-626-0272 for fastest service.

#### A high frequency divider from 500 Mhz to % Ghz+

The input interface.
The frequency divider has a differential analog interface. The following parameters apply:
The minimum frequency that can be input is 500 Mhz and the maximum frequency is 6.0 Ghz.
The RF input level is 5 dBm to – 5 dBm. For lower frequencies make sure that the slew rate is
greater than 560 V/us. The input is biased by two 500 Ohm resistors connected to a 1.6V DC bias.
Therefore AC coupling is used at the input. These are two 100pF capacitors.
The output interface.
The output is single ended. The output driver is capable of sourcing and sinking 24 mA. The
equivalent output impedance is 50 Ohm. To avoid reflections it is recommended that the divider
work into a 50 Ohm load.
General operation.
The inputs are applied to the input SMA I/O. The product will work with both a differential input as
well as a single ended input. However, a differential input works best. The division ratio is applied
to the N1 and N2 control inputs as follows:
N2 N1 Division ratio
0 0 8
0 1 16
1 0 32
1 1 64
The logic levels are:
Logic level Voltage
1 1.4V minimum
0 0.6V maximum
The supply voltage interface.
The operating supply voltage is 3.3V typical. The quiescent (DC) operating supply current is 2 mA.

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RF Switch typical features

Supply voltage = Vcc = 0/+5 Vdc
Operatng temperature = TA = -50° C to 125 Deg C
Operating impedance = 50 Ohm
Input power for 1 dB
compression ( 5.0V system) = 37 dBm ( f = 0.5 to 3 Ghz)
Input third order Intercept = 64 dBm ( 0 to 5.0V system, f = 0.5 to 3 Ghz)
Operating frequency range = DC to 3 Ghz.
Insertion loss DC to 3 Ghz = 0.8 dB
Isolation DC to 3 Ghz = 14 dB minimum
Return loss DC to 3 Ghz = 20 dB
50% contl to 10/90 %
( ON/OFF) = 120 ns

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Summary Specifications

Gain,  Operating: 19.5 dB
Operating frequency range: 1.0 – 2700 Mhz
OIP3: (Pout = 19.0 dBm),  -8.5 dBm
P1dB: 4.6 dBm
N.F: 4.2 dB
Supply voltage Operating: 3.3  – 5.5 Volts

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Free delivery, shipping lead time 2 days.

30 day return policy, buyer ships.
Supply current Supply = 5.0V,  23.0 mA