S parameter calculations for RF/Microwave design. Some comments on ARCTAN.

S parameters are usually used in calculations of RF/wireless/microwave design and development. S parameters are complex numbers that can be written in a rectangular form with real and imaginary components, as well as in the polar form, with a radius ( magnitude) and angle.

Conversions between the polar form and the rectangular form are common . Some engineers like the polar form others like the rectangular form. When converting from the rectangular form to the polar form, the magnitude is calculated by taking the square root of the sum of the squares of the real and imaginary component. Associated with this calculation is the angle.

The angle is calculated by taking the ARCTAN ( imaginary/real). This is easy to do but there is a wrinkle in this calculation that needs to be understood, and taken care of, when calculating the angle. We have found that some calculators on the web do not take care of this issue. 

The value of the angle is also dependent on the quadrant the angle lies in. For example, lets say that the real component is negative and the imaginary component is negative. When the imaginary is divided by the real in this case, the quotient is positive. When the ARCTAN is taken of this positive quantity the result can be ( if care is not taken) an angle in the first quadrant. This is misleading.

The correct result of such a calculation, must take account of which quadrant the angle lies in. In the above example the angle really lies in the third quadrant. The ARCTAN calculator can calculate the angle in the first quadrant. To get the correct answer one should subtract 180 degrees from the result.

Please see the Wikipedia for a detailed explanation of this. The search term is Inverse trigonometric functions.

At Signal Processing Group Inc., most of our RF/wireless/microwave designs use the s-parameter approach as routine. Please visit our website and check out other articles and information.

LNA

SPG designs, develops and delivers custom analog and RF/wireless asics and modules.

FPGA Design and development service

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

A wideband RF detector

A wideband RF detector

Linear detector performance

Linear detector performance curves

A wideband linear RF detector

Price for one unit: $25.00. Lead time for delivery 3 days. 30 Day return policy. Pricing for 100 units or more: $20.00 per unit.  Please contact Signal Processing Group Inc. for details for purchase from Signal Processing Group Inc. Email: spg@signalpro.biz 24/7

Wideband RF detector perforamce , more details

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2 stage 35 dB gain RF amplifier. Front of the module

Full range frequency response

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.

miniature LNA module

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.

A high frequency divider 500 Mhz to 5 Ghz+

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SPDT DC to 3 Ghz RF switch

DC to 3 Ghz RF SPDT switch

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

A single stage RF amplifier as a gain block

A single stage RF amplifier summary specifications

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

Price: single unit $7.50, 100 units : $5:50.

Free delivery, shipping lead time 2 days.

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

Embedded design and development

Signal Processing Group Inc. is offering embedded design and development using Microchip processors. Please contact us on spg@signalpro.biz for more information

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