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# How to design variable resistors R0 to represent the frequency-dependent loss in ADS

#### thundrous

##### Newbie level 4
I am trying to replicate a result of a paper in Advanced Design System software. It is mentioned that the resistance is variable and its equation is 10e-9f (GHz) + 5.

When I drew the resistance in the software and wrote the formula, a syntax error showed up.

Would you please guide me on how to enter this equation? Is there any specific module I need to enter inside the equation field?

Here is their equivalent circuit:

and here is the equivalent circuit that I drew:

#### dick_freebird

Seems like it just wants a wee bit of series L?

#### BigBoss

Use equation based s-parameter blocks.
Define first s-parameters matrix of a series resistor then enter these values into equation based blocks with the variable "freq". Otherwise it will not recognize.

#### thundrous

##### Newbie level 4
Use equation based s-parameter blocks.
Define first s-parameters matrix of a series resistor then enter these values into equation based blocks with the variable "freq". Otherwise it will not recognize.
Thank you very much for your response, until now I updated the equivalent circuit as follows, but still I cannot reach the proper data. Do you have any idea where the problem is? Also, i do not know how to introduce the frequency as the variable "freq". I tried to but the software does not accept it.
any suggestion appreciated.

#### thundrous

##### Newbie level 4
Seems like it just wants a wee bit of series L?
I do not know, would you please explain more?

#### BigBoss

S-parameters matrix of a series resistance ;

Then use equation based s-parameter block like this.

then you will see that s-parameters are not constant versus frequency. (If the resistance was constant, s-parameters should have been constant too but they aren't due to frequency dependence of the resistance)

#### thundrous

##### Newbie level 4
S-parameters matrix of a series resistance ;
View attachment 180869
Then use equation based s-parameter block like this.
View attachment 180870
then you will see that s-parameters are not constant versus frequency. (If the resistance was constant, s-parameters should have been constant too but they aren't due to frequency dependence of the resistance)
View attachment 180872
Thank you very much for your guidance I did what ever you mentioned in the previous comment as follows based on my current device and here is my Equivalent circuit:

S21, S11 are my experimental results and S65, S55 are for the simulation

I've got a good verification between S21 and S65, However the S55 does not seems good and it starts from -10dB
So based on the article I changed the frequency loss resistance depedance as follows: I eleiminated R=50

then the slope of S55 changed but still it starts from -10dB. It seems the variable Rlossy has lots of effect on our measurments and by changing the formula i even needed to change the capacitance C4 for validation between simulation and experiment results.

Would you please guide mewhich one is current and where did I made a mistake because S55 should start from zero.

#### Attachments

• 1674754604649.png
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#### BigBoss

It was my own example, not real/your one. You have to define your own formulae by yourself. It might
be anything as you desire. I dont know the process that you've been working on.