# Microwave filters: Lumped element design to transmission line equivalents

As frequencies increase in filters, lumped elements no longer satisfy the requirements for various reasons ( parasitics, accuracy etc). At this point the designer may choose to convert the lumped element filter to a distributed element filter. One of the techniques used is transmission line stubs in the conversion. This technique is described in a white paper released from Signal Processing Group Inc. recently. The paper may be found at http://www.signalpro.biz >> engineer’s corner by interested readers.

# RF Design: Electrical length

Sooner or later, the design engineer who is working in microwave or high frequency electronics, is going to come up against the concept of electrical length. In order to understand this concept lets work out the following arithmetic:

1.0 The wave number or phase constant = β = 2π/λ

For those unfamiliar with this, we recommend looking up the description of this quantity in the SPG blog at (http://signalpro-ain.blogspot.com/).

2.0 The electrical length is defined by θ = βl where l = physical length

3.0 θ = βl = (l/ λ) *360 degrees

Here λ is the wavelength of the signal in the applicable dielectric ( or sometimes called the guide wavelength).

4.0 For a frequencies in Ghz, this becomes: [360 * fGhz * l(cm) * √εeff]/30 cm

In this case frequency is in Ghz, physical length is in centimeters.

For example:

Let frequency be 1 Ghz.
Let λ = 0.8 λ(air) or √εeff = 1.25
Let l = 0.1 meters = 0.1E2 centimeters

Then :

θ = [360* 1*0.1E2*1.25]/30 degrees

θ = 150 degrees

# Analog design: Magnitude and frequency scaling in filter design

Not infrequently, filters are designed using a different scale for their component parts than the final requirement. For example a filter could be designed for a frequency of 1.0, inductors in Henries and capacitors in Farads. The Smith chart uses scaling as a matter of common usage. It becomes a vital part of the design engineer’s repertoire to understand this concept. This post deals with the very basics of scaling in a cookbook fashion for simplicity. Here are the rules: (1) If each inductor and capacitor is multiplied by a quantity 1/alpha, then the network is said to be scaled in frequency by alpha. If every resistance and inductance is multiplied by a quantity beta, and every capacitor is divided by beta, then the network is said to be magnitude scaled by beta.

# The wavenumber β or the phase constant

β is an important quantity used in understanding transmission lines and waveguides. It is not intuitive so this treatment presents a brief explanation of the quantity in the analysis of transmission lines, waveguide and other wave systems.

Sometimes β is referred to as the phase constant of the line or guide. If the cartesian coordinate system is used and a coordinate, say “z” is used as the direction of wave propagation then βz measures the instantaneous phase at point z on the line with respect to z =0.

In addition, voltage or current on the line is the same at any two points separated in z such that βz differs by multiples of 2π. Since the shortest distance between points where voltage or current is at the same phase is a wavelength, then:

βλ = 2π

( replacing z by λ),

β = 2π/λ

_____________________________________________________________

# Multi – chip in a package technology

When a designer has a system that is designed with chips with differing voltages, currents, frequencies and special characteristics it is difficult to integrate the system for cost or size reduction. In this case the usual approach is a motherboard – daughter board combination. ( Usually, but not always). Recently it appears that designers are turning to multi-chip in a package technology. In this case a package is used which has die in it assembled in a vertical configuration or a side by side combination. Properly done , this can be a powerful way of getting the job done in a shorter time with less cost than a difficult integration approach. The design of the multi-chip configuration is the key. Some parameters to be considered seriously are temperature effects, parasitic connections, grounding, and frequency performance. Signal Processing Group Inc., is offering a multi-chip in a package design and assembly service for interested users. SPG website is located at http://www.signalpro.biz.

# De-embedding in high frequency measurements

High frequency measurements for circuits such as MMICs and high speed digital circuits are made using some kind of Vector Network Analyzer ( VNA) or some kind of TDR instrument. In most cases the DUT ( device under test) is mounted on a test fixture which probably has an input connector and microstrip and an output connector and microstrip. The measurements are to be made on the characteristics of the DUT. To do this the test fixtures have to be de-embedded. This technique and its basics form the subject of the latest brief paper from the technical team at Signal Processing Group Inc. It can be found at http://www.signalpro.biz in the Engineer’s Corner.

# Note on bondwire fusing current paper

This is a note to confirm a reference quoted in an article in engineer’s corner on bondwire fusing current. The complete reference should read, J. Thomas May, Electrical Overstress – Electrostatic Discharge Symposium 1994.

# Useful identities for bipolar design

Bipolar design has been popular for a very long time. It continues to provide a device that is being used today in various forms. In standard bipolar processes, in combination with CMOS in BiCMOS processes, in high current designs, in high voltage with high current designs. Technology and device vendors keep improving their technologies and processes. Recently the advent of SiGe technology also provides a very high performance bipolar device. For the design engineer a set of identities which provides a way for simple hand calculations of the bipolar device for use in a circuit can be useful. Ultimately, the circuit design can be either breadboarded or simulated to evaluate performance. However, hand calculations can be and should be a first step. To facilitate this process the technical team at Signal Processing Group Inc., have recently released a brief paper on some useful bipolar design identities. This is available on the SPG website in the ” Engineer’corner”. Please visit http://www.signalpro.biz.