Wilkinson Splitter test case

[gadiLhv]

It took me a minute and a half to figure out how to operate the Lumped Element functionality without the PCB module, but I got it to work.

A few notes:

1. Can you allow to copy the body in "rotate"?
2. Is there a better way to assign PEC B.C. to multiple bodies, than this? It also took me a while to figure out that assigning metal properties to a sheet wasn't enough.

# All metals a PEC, for now...
pec_gnd = model.mw.bc.PEC(gnd_bot)
pec_circ = model.mw.bc.PEC(traceCirc)
pec_feed = model.mw.bc.PEC(feed)
pec_out_1 = model.mw.bc.PEC(out_1)
pec_out_2 = model.mw.bc.PEC(out_2)
pec_pads = model.mw.bc.PEC(res_pads)

3. Is it possible to do something like "lossy metal" boundary conditions, e.g.

And in general, the results don't make any sense to me. I'd appreciate if you'd take a look. I verified this design in a different software prior to this simulation.

import emerge as em
from emerge.plot import plot_sp
import numpy as np


def Rf(R):
    return lambda f: R

# Unit definitions 
mm = 0.001               # meter per millimeter
mil = 0.0254 * mm        # meter per mil (thousandth of an inch)


# Frequency range
f1 = 5e9            # Start frequency [Hz]
f2 = 15e9           # Stop frequency [Hz]
Nf = 25             # Number of frequency samples

# Balancing resistor
Rwilk = 100 # [Ohm]

# Geometry parameters
MSL_W = 1.05*mm            # reference trace width [mm]
MSL_70_W = 0.575*mm          # Trace width for 70 Ohm (50*sqrt(2)) [mm]

Sub_Thick = 0.5*mm         # Substrate thickness (mm)

Sub_Dk = 3.5
Sub_W = 25*mm              # Substrate width(mm)
Sub_L = 25*mm              # Substrate width(mm)

Feed_L = 3.5*mm
Out_L = 4*mm

Wilk_Split_Rad = 5.4*mm

Wilk_Res_Pads_D = 0.4*mm
Wilk_Res_W = 0.5*mm
Wilk_Res_Pad_W = 0.6*mm
Wilk_Res_Pad_L = 0.6*mm 

Air_H = 5*mm                # Height of air above PCB

Mesh_Wilk_Edge_Step = 0.25*mm
Mesh_Traces_Edge_Step = 0.4*mm

# Name this build
model = em.Simulation('Wilkinson_11GHz', loglevel='DEBUG')

########################
# Geometry Definitions #
########################

# Create PCB layouter with given substrate thickness and units
substrate = em.geo.Box(Sub_W, Sub_L, Sub_Thick,
                        position=(-Sub_W*0.5, 0, 0))

airbox = em.geo.Box(Sub_W,Sub_L,Air_H,position=(-Sub_W*0.5,0,Sub_Thick))

gnd_bot = em.geo.XYPlate(Sub_W,Sub_L,position=(-Sub_W*0.5,0,0))

substrate = em.geo.translate(substrate,0,-Sub_L*0.5 + Feed_L + Wilk_Split_Rad,0)
gnd_bot = em.geo.translate(gnd_bot,0,-Sub_L*0.5 + Feed_L + Wilk_Split_Rad,0)
airbox = em.geo.translate(airbox,0,-Sub_L*0.5 + Feed_L + Wilk_Split_Rad,0)

##############
# Build feed #
##############

feed = em.geo.XYPlate(MSL_W,Feed_L,position=(-MSL_W*0.5,0,Sub_Thick))

#########################
# Build splitter traces #
#########################


# Circle radii
outRad = Wilk_Split_Rad + MSL_70_W*0.5
inRad = Wilk_Split_Rad - MSL_70_W*0.5

inCirc = em.geo.Disc((0,Feed_L + Wilk_Split_Rad,Sub_Thick),inRad,(0,0,1))
traceCirc = em.geo.Disc((0,Feed_L + Wilk_Split_Rad,Sub_Thick),outRad,(0,0,1))
traceCirc = em.geo.remove(traceCirc, inCirc)


feed = em.geo.remove(feed,traceCirc,remove_tool=False)

#######################
# Build resistor pads # 
#######################

res_pads = em.geo.XYPlate(Wilk_Res_Pad_L*2.0 + Wilk_Res_Pads_D, Wilk_Res_Pad_W,position=(-(Wilk_Res_Pad_L*2.0 + Wilk_Res_Pads_D)*0.5,Feed_L+Wilk_Split_Rad*2.0 - Wilk_Res_Pad_W*0.5,Sub_Thick))

# Remove pads (and gap) from splitter traces 
traceCirc = em.geo.remove(traceCirc,res_pads,remove_tool=False)

# Cutout gap in traces
res_pads_cutout = em.geo.XYPlate(Wilk_Res_Pads_D, Wilk_Res_Pad_W*2,position=(-Wilk_Res_Pads_D*0.5,Feed_L+Wilk_Split_Rad*2.0 - Wilk_Res_Pad_W,Sub_Thick))
res_pads = em.geo.remove(res_pads,res_pads_cutout,remove_tool=False)

#################
# Build outputs # 
#################

cutoutCirc = em.geo.Disc((0,Feed_L + Wilk_Split_Rad,Sub_Thick),outRad,(0,0,1))

out_1 = em.geo.XYPlate(MSL_W, Out_L, position=(-MSL_W*0.5, 0, Sub_Thick))
out_1 = em.geo.rotate(out_1, (0,0,0), (0,0,1), 45)
out_1 = em.geo.translate(out_1, (Wilk_Res_Pad_L + Wilk_Res_Pads_D)*0.5, Feed_L+Wilk_Split_Rad*2.0, 0)
out_2 = em.geo.mirror(out_1,(0,0,0),(1,0,0),make_copy=True)

out_1 = em.geo.remove(out_1,res_pads,remove_tool=False)
out_2 = em.geo.remove(out_2,res_pads,remove_tool=False)
out_1 = em.geo.remove(out_1,traceCirc,remove_tool=False)
out_2 = em.geo.remove(out_2,traceCirc,remove_tool=False)
out_1 = em.geo.remove(out_1,res_pads_cutout,remove_tool=False)
out_2 = em.geo.remove(out_2,res_pads_cutout,remove_tool=True)
out_1 = em.geo.remove(out_1,cutoutCirc,remove_tool=False)
out_2 = em.geo.remove(out_2,cutoutCirc,remove_tool=True)

################################
# Build Lumped port primitives # 
################################

# Port #1
port_1_feed = em.geo.Plate((-MSL_W*0.5,0,0),(MSL_W,0,0),(0,0,Sub_Thick))
port_2_out = em.geo.Plate((-MSL_W*0.5,Out_L,0),(MSL_W,0,0),(0,0,Sub_Thick))

port_2_out = em.geo.rotate(port_2_out,(0,0,0),(0,0,1),45)
port_2_out = em.geo.translate(port_2_out, (Wilk_Res_Pad_L + Wilk_Res_Pads_D)*0.5, Feed_L+Wilk_Split_Rad*2.0, 0)

port_3_out = em.geo.mirror(port_2_out,(0,0,0),(1,0,0),make_copy=True)

port_4_res = em.geo.XYPlate(Wilk_Res_Pads_D, Wilk_Res_Pad_W,position=(-Wilk_Res_Pads_D*0.5,Feed_L+Wilk_Split_Rad*2.0 - Wilk_Res_Pad_W*0.5,Sub_Thick))

####################
# Assign materials #  
####################

substrate.material = em.Material(Sub_Dk, tand=0.01,
                                  color="#207020", opacity=0.3)

feed.material = em.lib.MET_COPPER
gnd_bot.material = em.lib.MET_COPPER
traceCirc.material = em.lib.MET_COPPER
res_pads.material = em.lib.MET_COPPER
out_1.material = em.lib.MET_COPPER
out_2.material = em.lib.MET_COPPER
airbox.material = em.lib.AIR


###################
# Mesh refinement #
###################

model.mw.resolution = 0.2
model.mw.set_frequency_range(f1,f2,Nf)

model.commit_geometry()


model.mesher.set_boundary_size(traceCirc, Mesh_Wilk_Edge_Step, 1.1)
model.mesher.set_boundary_size([feed,res_pads,out_1,out_2], Mesh_Traces_Edge_Step, 1.1)

# Generate mesh
model.generate_mesh()

####################
# Port assignemnts #
####################
port_1_feed = model.mw.bc.LumpedPort(
    port_1_feed, 1,
    width=MSL_W, height=Sub_Thick,
    direction=em.ZAX,
    active=True, Z0=50
)

port_2_out = model.mw.bc.LumpedPort(
    port_2_out, 2,
    width=MSL_W, height=Sub_Thick,
    direction=em.ZAX,
    active=True, Z0=50
)


port_3_out = model.mw.bc.LumpedPort(
    port_3_out, 3,
    width=MSL_W, height=Sub_Thick,
    direction=em.ZAX,
    active=True, Z0=50
)

# le_sel = model.geo.selection
le_4_res = model.mw.bc.LumpedElement(port_4_res.boundary(),
                                     Rf(Rwilk),
                                     Wilk_Res_Pads_D,
                                     Wilk_Res_Pad_W)


###########################
# Set boundary conditions #
###########################

# Top side is ABC
abc = model.mw.bc.AbsorbingBoundary(airbox.outside('top'))

# All metals a PEC, for now...
pec_gnd = model.mw.bc.PEC(gnd_bot)
pec_circ = model.mw.bc.PEC(traceCirc)
pec_feed = model.mw.bc.PEC(feed)
pec_out_1 = model.mw.bc.PEC(out_1)
pec_out_2 = model.mw.bc.PEC(out_2)
pec_pads = model.mw.bc.PEC(res_pads)


##################
# Run simulation #
##################


# View model before simulation
model.view()

model.mw.frequency_domain()
data = model.mw.data

################
# Post process #
################



freqs = data.scalar.grid.freq
f_fit = np.linspace(f1, f2, 2001) 
S11 = data.scalar.grid.model_S(1, 1,f_fit)            # reflection coefficient
S21 = data.scalar.grid.model_S(2, 1,f_fit)
S31 = data.scalar.grid.model_S(3, 1,f_fit)
plot_sp(f_fit / 1e9, [S11,S21,S31],labels=['S11', 'S21','S31'])                 # plot return loss in dB

[FennisRobert]

I'll answer your questions first.

1. I happen to need that functionality not too long ago too. I think itll be more of the kind: new_obj = em.geo.rotate(first_obj.copy(), ...)
2. There is not yet a very efficient way but i'll make one soon so that you can just bundle all these objects together and pass them once. It'll be on the todo.
3. Yes allthough I haven't verified yet that its exactly the same boundary condition but you can use SurfaceImpedance boundary condition and assign a material to it. It takes into account skin effects

[FennisRobert]

Couple of other points

EMerge doesn't care if surfaces of stripline sections overlap. So you dont have to use all these remove operations.

If you read the documentation(in your IDE) for the function .outside() you will read that the arguments determine which boundaries are not included. Granted this is not very intuitive. So outside("top") takes all boundaries except the top. If you want to select only the top you use .face('top'). I might pick a better name for .outside().

On this line: le_4_res = model.mw.bc.LumpedElement(port_4_res.boundary(), you don't have to use .boundary(). You can just pass the object.

If I remove the absorbing boundary condition it works.

[gadiLhv]

I was pretty sure I tried it without the .boundary() and it didn't work. Probably some other mistake along the way.

One more clarification: I wanted to add the absorbing B.C. on the top face, because I saw in another software (the commercial kind) that it causes instability in the S-Parameter convergence if I go all-electric. The simulation converges, but the broadband sweep, doesn't.

Next step, with Modal ports (I hate HFSS terminology).

Cheers, and thanks again, @FennisRobert!

[FennisRobert]

Ill check to make sure then if it wasnt an emerge problem. I get that you wanted the abc. It was a quick test. Although just replacing .outside with .face would have been equally fast :p

…

On Mon, 18 Aug 2025 at 23:18, Gadi Lahav ***@***.***> wrote: I was pretty sure I tried it without the .boundary() and it didn't work. Probably some other mistake along the way. One more clarification: I wanted to add the absorbing B.C. on the top face, because I saw in another software (the commercial kind) that it causes instability in the S-Parameter convergence if I go all-electric. The simulation converges, but the broadband sweep, doesn't. Next step, with Modal ports (I hate HFSS terminology). Cheers, and thanks again, @FennisRobert <https://github.com/FennisRobert>! image.png (view on web) <https://github.com/user-attachments/assets/57d41d31-a222-42c1-b401-ae6d7360eb40> — Reply to this email directly, view it on GitHub <#9 (reply in thread)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/A4EZODJ4EBTKZ7VB4VD5YKL3OI7JJAVCNFSM6AAAAACEGDDZ6SVHI2DSMVQWIX3LMV43URDJONRXK43TNFXW4Q3PNVWWK3TUHMYTIMJUGYZTSNQ> . You are receiving this because you were mentioned.Message ID: ***@***.***>

[FennisRobert]

Hey Gadi,

First apologies for being a bit rude in my previous comment. I really appreciate you trying EMerge.

This exchange has been very helpful and I think I've made EMerge a bunch better. For the next version the following improvements are made:

1. There is the emerge.select(...) function so that you can just pass all the objects inside them:

pec_gnd = model.mw.bc.PEC(em.select(gnd_bot, traceCirc, feed, out_1, out_2, res_pads))

2. The function .outside() is renamed and reformulated so that you now do .boundary(exclude=('top',)). So exclusions are explicitly named as a named argument to prevent confusion.
3. There is now also a em.geo.unite(obj1, obj2, obj3) function that you can just pass objects to to unite them into one shape without internal boundaries. Convenient to just merge your striplines into one object without having to remove them and it removes the internal overlapping boundaries.
4. .rotate and .translate now also have the make_copy optional argument to make the copies :)

[gadiLhv]

If there was something rude, I probably missed it. I have this ability to take the necessary parts of texts, ignoring the rest. Browsing through hunderds of garbage IEEE articles will do that to ya :)

1. Thank you for the em.select advice, I was looking for a way to generate a selection, now I know how.
2. The switch to face() instead of outside() already did the trick yesterday, but appreciate the update alltoegther.
3. I am familiar with the boolean unite, but I wanted different local mesh optimizations for the splitter and the rest of the traces.
4. That, is a great update!

Cheers, and massive respect for the excellent work! Linkedin post already scheduled later today.
In the next tests I'll probably have more inputs.

[FennisRobert]

I just added em.select, it didn't exist yet :). If people interpret the functions I make wrong then I think its a good signal that the purpose of the function is ambiguous so I think this clarification is sensible. I also understand where the mis-interpretation comes from.
.unite(...) in its form is new! I had add but it only allowed you to unite two. But beyond that, I do get why you made that choice. Adaptive mesh refinement should resolve a lot of these manual mesh problems :).

Already thanks for the linked-in post! Its much appreciated.