By Wolfgang Höß 27. February 1997

The computer simulation of RF-circuits is an important aspect of any RF and microwave design. At microwave frequencies there are no ideal devices available. A chip capacitor, for instance, shows a series resonance at higher frequencies. For accurate RF-simulations one has to find the right models for each element one is using. This paper describes the high frequency models of passive lumped elements. It includes the parameter extraction of the used printed circuit board, SMA-connectors, resistors, capacitors and RF-coils, based on S-parameter measurements. Also, comparison between measurements and computer simulations are made.

**1. Used equipment:**

HP8573C | Network analyzer |

HP85047A | S parameter test set |

HP34401A | Multi Meter |

HP8573C.EXE | PC-Labview program to transfer the measured S-parameters from the Network analyzer to a PC |

MDS6.50 | RF-Simulation program |

**2. Network analyzer calibration:**

Network analyzer calibration settings:

Frequency: | 300kHz-3GHz (50MHz - 6GHz) |

Source power: | 0dBm (+20dBm) |

Attenuators: | 0dBm |

IF bandwidth: | 10Hz |

port1: | male cal kit |

port2: | worm and the female cal kit |

following port extensions are used:

Port1: | 59.148ps | (17.732mm) |

Port2: | 16.926ps | (5.0743mm) |

The modeling procedure is based on S-parameter measurements. The high frequency behavior of the devices is measured in a strip line configuration. A test board with distributed line elements, as transmission lines, open stubs, shorted stubs and transmission lines with specific structures for SMD elements is used for these measurements. First it is necessary to characterize the used FR4 material:

FR4 material data from the manufacturer:

er: | 4.7, substrate permittivity |

tan d: | better 0.03 |

w50: | 0.595mm, width for a 50Ohm transmission line |

h: | 0.360mm, substrate thickness |

t: | 35mm (thickness of the copper) |

The er of the material is fitted by the resonance frequency. The tan d of the print material is fitted by the width of the resonance curve (equal to the Q of the resonator).

Results of the extraction:

er: | 4.71 |

tand: | 0.027 |

Fig.1: Line resonator Schematic

Fig.2: Line resonator transfer function S21

**3.1 SMA-connector model**

The next step is to find a model for the SMA-connector. All connectors are soldered on the test board. There is a transition from the coaxial wave guide to the transmission line wave guide. The SMA Connector is modeled by a lossy scattering capacitor model [2] with coaxial cables. This was verified by measuring distributed line elements like a transmission line, two shorted stubs with VIA's and two open stubs.

Fig.3: SMA-Connector model

By working with this model it turns out that it would be better to implement
a small transmission line to the SMA-connector into the model to implement
a better fit of the mode transition. One diadvantage of this method is
that the SMA-model is dependent on the the used PCB-material. (er, tand
and the geometric dimension). Also, it would be good improvement
to solder the SMA-Connector in the direction of the transmission line.

used SMA connector soldering configuration

a better SMA connector soldering configuration

Verification of the SMA-connector model with distributed transmission
lines. (open stub and via grounded stub [3])

Fig.4: Verification of the SMA-model

Comparison between measurement and simulation:

Fig.5: Presentation

**4. Lumped element models**

The parameter extraction based on measurements in a strip line configuration
as shown below.

Two different configurations are used:

DUT
is soldered into the signal path of the transmission line ('SHUNT')

DUT
is soldered from the middle of the transmission line to the ground ('SERIES')

For the parameter extraction the s-parameters was measured in 'Shunt' and 'Series' configuration.The s-parameters are measured with a HP8573C-Networkanalyzer. Additional a Labview program (named HP8753C) was used to transfer the S-parameters, in CITI-file format to a PC.

**4.1 Resistor model**

Following resistors are measured:

Roederstein 0805 1% (0, 10, 51, 100 and 910Ohm)

To reduce measurement work, only a small amount of resistors are modeled.
The model consist a frequency dependent resistor (for the skin effect),
a series inductor and and a parallel scattering capacitor,as shown below
in Figure 6.

The DC-resistance was measured by a 4-wire Kelvin measurement with the HP34401A.

Fig.8: Jumper Presentation

The resistor model shows that the series inductance can be extracted
for small resistors (<<50). For higher resistors (>500 Ohm) the impedance
of the series inductor becomes less than the resistance. It turned out
that the SMA-connector model has a significant influence to the extracted
resistor parameters. The modeled frequency dependence faktor k can be neglected
for resistors. Only the jumper (0 Ohm resistor) showes a higher k factor.

Results for Jumpers and Resistors:

Table 1.

**4.2 Capacitor model**

used ceramic SMD capacitors: Roederstein NPO PCC101P 0805 1pF - 1nF

Ceramic multilayer capacitors are suitable for use at high frequencies. At frequencies below the series resonance frequency, the capacitor can be represented by an equivalent cirucuit as shown in Fig. 9. In general, the quantities C, R and L are frequency dependent. For most applications, C and L can be regarded as frequency independent (true below 1GHz). The series resistance R is the equivalent series resistance which is determined by energy dissipation mechanisms (in the dielectric material as well as in the electrodes). The series inductance L models the change in effective capacitance up to the first series resonance. This means that this model is accurate up to the first resonance. The frequency region above the self resonance frequency is difficult to model by using lumped elements and should be described in terms of network of transmission lines. However, a lumped element model is easier to implement in simulator like Cadence SPECTRE or SPICE.

Table 2. Capacitor model parameters

Table 2 shows the parameters for Roederstein capacitors. The last column fres is the calculated capacitor series resonance frequency. Capacitors lower 3.9pF are measured in a frequency range from 50MHz - 6GHz, capacitors above 3.9pF are measured in a frequency range from 300kHz - 3GHz. Above 150pF additional resonances appear. The capacitors consist of a rectangular block of ceramic dielectric in which a number of interleaved metal electrodes are contained. This structures gives rise to a high capacitance per unit volume. The inner electrodes are connected to the two terminations. The additional resonances are parallel resonances from couplings between the inner metal layers [6].

Fig.10: Equivalent series inductance L as function of the capacitance

Fig.11: Equivalent series resistance R as function of the capacitance

Fig.12: Series resonance frequency as a function of capacitance

The quality factor Q of the capacitor is given by:

Fig.13: Quality factor Q as a function of the capacitance

Fig.13: MDS Schematic of the Parameter extraction for a 10pF capacitor

Fig.14: MDS Presentation for a 10pf capacitor

Capacitor model fitting functions:[C]=pF. The series inductivity L is fitted in two ways. Lchip is the direct fit of the extracted L. Lnom is the fitted inductivity from the measured series frequency. Lnom should be used for simulations and optimizations.

(this function is calculated
from fres and C)

(this
function models the extracted inductivity)

(fres is calculated from
the extracted parameters Cchip and Lchip)

**4.2 Coil model**

used ceramic SMD coils: Coilcraft inductors 0805CS series (2012) 3.3nH - 220nH

The coil model includes a inductor Lchip with a frequency dependent
resistor Rchip and a scattering capacitor Cchip. The resistor models the
DC-resistance of the wire and the skineffect resistance at high frequencies.
A 4 wire Kelvin measurement is used to measure the DC-resistance Rdc (HP34401A
Multimeter). The capacitor Cchip models the coupling between the turns
of the wire and the pad capacitance.

Fig.15: Coil model

Tab.2: Extracted coil model parameters

Fig.16: Measured coil DC-resistance

Fig.17: Extracted capacitance Cchip=f(L)

Fig.18: Skin effect factor k = f(L)

Coilcraft model fitting functions:

These fitting functions are useful for optimisations. The skin effect faktor k increases very much for Coils smaller then 15nH. There could be a problem in the model or the parameter extraction procedure. Also all extracted coils have a lower extracted inductivity as nominal. So handle this values very carefully. The parameter extraction will be repeated as soon as possible with a new testboard.

**4.2.2 Alternative coil model extracted from datasheet parameters**

This chapter describes a parameter extraction procedure based on datasheet
parameters and was devised by Klaus Peter Tschernay. Some parameters taken
from the datasheet are maximum values and some parameter are typical values.
Therefore some parameters from the extracted model shows not the real value
the device but represents the worst case (RDC ). By the way the parameter
extraction of this model is very simple and the simulation results are

very accurate.

Coilcraft chip inductors 0805HS Series

**A Datasheets:** Coilcraft coils: www.coilcraft.com
Roederstein capacitors: www.vishay.com

**References:**

1 On the Solution of a Microstripline
with two dielectrics, IEEE transactions on microwave theory and techniques,
Vol 32, No. 4, April 84

2 A Broad-Band model for a coaxial-to-stripline
transition, IEEE transactions on microwave theory and techniques, Vol 28,
No. 2, February 80

3 Modeling via hole grounds in
microstrip, IEEE microwave and guided wave letters, Vol. 1, No. 6, June
91

4 Analysis of microwave capacitors
and IC packages IEEE transactions on microwave theory and techniques, Vol
42, No. 9, September 94

5 A high frequency model based
on the physical structure of the ceramicmultilayer capacitor, IEEE
transactions on microwave theory and techniques, Vol 40, No. 7, July 92

6 Chip capacitor dielectric
effects on hybrid microwave amplifiers ISHM Conf. Rec. Oct. 1971

7 Modeling Inductors in PSPICE
Coilcraft, Document 158 Rev. 7/13/95