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# Circuit Design

## Intro

mwavepy has basic support for microwave circuit design. Network synthesis is accomplished through the Media Class (`mwavepy.media`), which represent a transmission line object for a given medium. A Media object contains properties such as propagation constant and characteristic impedance, that are needed to generate network components.

Typically circuit design is done within a given frequency band. Therefore every Media object is created with a Frequency object to relieve the user of repitously providing frequency information for each new network created.

## Media’s Supported by mwavepy

Below is a list of mediums types supported by mwavepy,

- DistributedCircuit
- Freespace
- RectangularWaveguide
- CPW

More info on all of these classes can be found in the media sub-module section of `mwavepy.media` mavepy’s API.

Here is an example of how to initialize a Media object representing a freespace from 10-20GHz:

    import mwavepy as mv
    freq = mv.Frequency(10,20,101,'ghz')
    my_media = mv.media.Freespace(freq)

Here is another example constructing a coplanar waveguide media. The instance has a 10um center conductor and gap of 5um, on a substrate with relative permativity of 10.6,:

    freq = mv.Frequency(500,750,101,'ghz')
    my_media = mv.media.CPW(freq, w=10e-6, s=5e-6, ep_r=10.6)

or a WR10 Rectangular Waveguide:

    from scipy.constants import * # for the 'mil' unit
    freq = mv.Frequency(75,110,101,'ghz')
    my_media = mv.media.RectangularWaveguide(freq, a=100*mil)

## Creating Individual Networks

Network components are created through methods of a Media object. Here is a brief, incomplete list of a some generic network components mwavepy supports,

- match
- short
- open
- load
- line
- tee
- thru
- delay_short
- shunt_delay_open

Details for each component and usage help can be found in their doc-strings. So help(my_media.short) should provide you with enough details to create a short-circuit component. To create a 1-port network for a short,

    my_media.short()

to create a 90deg section of transmission line, with characteristic impedance of 30 ohms:

    my_media.line(d=90,unit='deg',z0=30)

Network components specific to a given medium, such as cpw_short, or microstrip_bend, are implemented in by the Media Classes themselves.

## Building Cicuits

Circuits can be built in an intuitive maner from individual networks. To build a the 90deg delay_short standard can be made by:

    delay_short_90deg = my_media.line(90,'deg') ** my_media.short()

For frequently used circuits, it may be worthwhile creating a function for something like this:

    def delay_short(wb,*args,**kwargs):
            return my_media.line(*args,**kwargs)**my_media.short()

    delay_short(wb,90,'deg')

This is how many of mwavepy’s network compnents are made internally.

To connect networks with more than two ports together, use the connect() function. You must provide the connect function with the two networks to be connected and the port indecies (starting from 0) to be connected.

To connect port# ‘0’ of ntwkA to port# ‘3’ of ntwkB:

    ntwkC = mv.connect(ntwkA,0,ntwkB,3)

Note that the connect function takes into account port impedances. To create a two-port network for a shunted delayed open, you can create an ideal 3-way splitter (a ‘tee’) and conect the delayed open to one of its ports, like so:

    tee = my_media.tee()
    delay_open = my_media.delay_open(40,'deg')

    shunt_open = connect(tee,1,delay_open,0)

## Single Stub Tuner

This is an example of how to design a single stub tuning network to match a 100ohm resistor to a 50 ohm environment.

    # calculate reflection coefficient off a 100ohm
    Gamma0 = mv.zl_2_Gamma0(z0=50,zl=100)

    # create the network for the 100ohm load
    load = my_media.load(Gamma0)

    # create the single stub  network, parameterized by two delay lengths
    # in units of 'deg'
    single_stub = my_media.shunt_delay_open(120,'deg') ** my_media.line(40,'deg')

    # the resulting network
    result = single_stub ** load

    result.plot_s_db()

## Optimizing Designs

The abilities of scipy’s optimizers can be used to automate network design. To automate the single stub design, we can create a ‘cost’ function which returns somthing we want to minimize, such as the reflection coefficient magnitude at band center.

    from scipy.optmize import fmin

    # the load we are trying to match
    load = my_media.load(mv.zl_2_Gamma0(100))

    # single stub generator function
    def single_stub(wb,d0,d1):
            return my_media.shunt_open(d1,'deg')**my_media.line(d0,'deg')

    # cost function we want to minimize (note: this uses sloppy namespace)
    def cost(d):
            return (single_stub(wb,d[0],d[1]) ** load)[100].s_mag.squeeze()

    # initial guess of optimal delay lengths in degrees
    d0= 120,40 # initial guess

    #determine the optimal delays
    d_opt = fmin(cost,(120,40))

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