# Lumped Elements Circuits¶

In this notebook, we construct various network from basic lumped elements (resistor, capacitor, inductor), with the ‘classic’ and the `Circuit`

approach. Generally the `Circuit`

approach is more verbose than the ‘classic’ way for building a circuit. However, as the circuit complexity increases, in particular when components are connected in parallel, the `Circuit`

approach is interesting as it increases the readability of the code. Moreover, `Circuit`

object can be plotted using its
`plot_graph()`

method, which is usefull to rapidly control if the circuit is built as expected.

```
[1]:
```

```
import numpy as np # for np.allclose() to check that S-params are similar
import skrf as rf
rf.stylely()
```

## LC Series Circuit¶

In this section we reproduce a simple equivalent model of a capacitor \(C\), as illustrated by the figure below:

```
[2]:
```

```
# reference LC circuit made in Designer
LC_designer = rf.Network('designer_capacitor_30_80MHz_simple.s2p')
```

```
[3]:
```

```
# scikit-rf: manually connecting networks
line = rf.media.DefinedGammaZ0(frequency=LC_designer.frequency, z0=50)
LC_manual = line.inductor(24e-9) ** line.capacitor(70e-12)
```

```
[4]:
```

```
# scikit-rf: using Circuit builder
port1 = rf.Circuit.Port(frequency=LC_designer.frequency, name='port1', z0=50)
port2 = rf.Circuit.Port(frequency=LC_designer.frequency, name='port2', z0=50)
cap = rf.Circuit.SeriesImpedance(frequency=LC_designer.frequency, name='cap', z0=50,
Z=1/(1j*LC_designer.frequency.w*70e-12))
ind = rf.Circuit.SeriesImpedance(frequency=LC_designer.frequency, name='ind', z0=50,
Z=1j*LC_designer.frequency.w*24e-9)
# NB: it is also possible to create 2-port lumped elements like:
# line = rf.media.DefinedGammaZ0(frequency=LC_designer.frequency, z0=50)
# cap = line.capacitor(70e-12, name='cap')
# ind = line.inductor(24e-9, name='ind')
connections = [
[(port1, 0), (cap, 0)],
[(cap, 1), (ind, 0)],
[(ind, 1), (port2, 0)]
]
circuit = rf.Circuit(connections)
LC_from_circuit = circuit.network
```

```
[5]:
```

```
# testing the equivalence of the results
print(np.allclose(LC_designer.s, LC_manual.s))
print(np.allclose(LC_designer.s, LC_from_circuit.s))
```

```
True
True
```

```
[6]:
```

```
circuit.plot_graph(network_labels=True, edge_labels=True, port_labels=True)
```

## A More Advanced Equivalent Model¶

In this section we reproduce an equivalent model of a capacitor \(C\), as illustrated by the figure below:

```
[7]:
```

```
# Reference results from ANSYS Designer
LCC_designer = rf.Network('designer_capacitor_30_80MHz_adv.s2p')
```

```
[8]:
```

```
# scikit-rf: usual way, but this time this is more tedious to deal with connection and port number
freq = LCC_designer.frequency
line = rf.media.DefinedGammaZ0(frequency=freq, z0=50)
elements1 = line.resistor(1e-2) ** line.inductor(24e-9) ** line.capacitor(70e-12)
elements2 = line.resistor(20e6)
T_in = line.tee()
T_out = line.tee()
ntw = rf.connect(T_in, 1, elements1, 0)
ntw = rf.connect(ntw, 2, elements2, 0)
ntw = rf.connect(ntw, 1, T_out, 1)
ntw = rf.innerconnect(ntw, 1, 2)
LCC_manual = ntw ** line.shunt_capacitor(50e-12)
```

```
[9]:
```

```
# scikit-rf: using Circuit builder
freq = LCC_designer.frequency
port1 = rf.Circuit.Port(frequency=freq, name='port1', z0=50)
port2 = rf.Circuit.Port(frequency=freq, name='port2', z0=50)
line = rf.media.DefinedGammaZ0(frequency=freq, z0=50)
cap = line.capacitor(70e-12, name='cap')
ind = line.inductor(24e-9, name='ind')
res_series = line.resistor(1e-2, name='res_series')
res_parallel = line.resistor(20e6, name='res_parallel')
cap_shunt = line.capacitor(50e-12, name='cap_shunt')
ground = rf.Circuit.Ground(frequency=freq, name='ground', z0=50)
connections = [
[(port1, 0), (res_series, 0), (res_parallel, 0)],
[(res_series, 1), (cap, 0)],
[(cap, 1), (ind, 0)],
[(ind, 1), (cap_shunt, 0), (res_parallel, 1), (port2, 0)],
[(cap_shunt, 1), (ground, 0)],
]
circuit = rf.Circuit(connections)
LCC_from_circuit = circuit.network
```

```
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```

```
# testing the equivalence of the results
print(np.allclose(LCC_designer.s, LCC_manual.s))
print(np.allclose(LCC_designer.s, LCC_from_circuit.s))
```

```
True
True
```

```
[11]:
```

```
circuit.plot_graph(network_labels=True, edge_labels=True, port_labels=True)
```

## Pass band filter¶

Below we construct a pass-band filter, from an example given in Microwaves101:

```
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```

```
# Reference result calculated from Designer
passband_designer = rf.Network('designer_bandpass_filter_450_550MHz.s2p')
```

```
[13]:
```

```
# scikit-rf: the filter by cascading all lumped-elements
freq = passband_designer.frequency
passband_manual = line.shunt_capacitor(25.406e-12) ** line.shunt_inductor(4.154e-9) ** \
line.capacitor(2.419e-12) ** line.inductor(43.636e-9) ** \
line.shunt_capacitor(25.406e-12) ** line.shunt_inductor(4.154e-9)
```

```
[14]:
```

```
# scikit-rf: the filter with the Circuit builder
freq = passband_designer.frequency
line = rf.media.DefinedGammaZ0(frequency=freq)
C1 = line.capacitor(25.406e-12, name='C1')
C2 = line.capacitor(2.419e-12, name='C2')
C3 = line.capacitor(25.406e-12, name='C3')
L1 = line.inductor(4.154e-9, name='L1')
L2 = line.inductor(43.636e-9, name='L2')
L3 = line.inductor(4.154e-9, name='L3')
port1 = rf.Circuit.Port(frequency=freq, name='port1', z0=50)
port2 = rf.Circuit.Port(frequency=freq, name='port2', z0=50)
ground = rf.Circuit.Ground(frequency=freq, name='ground', z0=50)
connections = [
[(port1, 0), (C1, 0), (L1, 0), (C2, 0)],
[(C2, 1), (L2, 0)],
[(L2, 1), (C3, 0), (L3, 0), (port2, 0)],
[(C1, 1), (C3, 1), (L1, 1), (L3, 1), (ground, 0)],
]
circuit = rf.Circuit(connections)
passband_circuit = circuit.network
passband_circuit.name = 'Pass-band circuit'
```

```
[15]:
```

```
passband_circuit.plot_s_db(m=0, n=0, lw=2)
passband_circuit.plot_s_db(m=1, n=0, lw=2)
passband_designer.plot_s_db(m=0, n=0, lw=2, ls='-.')
passband_designer.plot_s_db(m=1, n=0, lw=2, ls='-.')
```

```
[16]:
```

```
circuit.plot_graph(network_labels=True, port_labels=True, edge_labels=True)
```

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```

```
```