In trying to find a printable Smith chart, I was again disappointed in available online versions.
Nonetheless, the Smith chart remains a standard way of displaying reflection measurements on test instruments, and the paper version is occasionally used for quick problems. Like reactance paper, it allows for solving classes of problems without tedious calculations, but it has also been supplanted by the use of computers that produce exact results quicker. The Smith chart is useful for understanding transmission line dynamics and designing antenna matching networks in RF engineering. I found that a frequency range of 1 kHz to 1 GHz, and an impedance range of 100 mΩ to 1 MΩ covered the majority of typical analog circuits.Īnother well known nomogram used in electrical engineering is the Smith chart. I borrowed the color scheme used on FAA airspace charts, since they have a useful, but muted contrast. I made my own using PGF/TikZ, a graphics layer built on TeX \TeX T E X that is well suited for technical illustrations. I found working with reactance paper so helpful for quickly characterizing passive networks that I wanted to have a notepad of them, but I found only mediocre versions online. All of this can be read easily from the chart by the following the minimum of the asymptotes, the overdamped behavior and pole frequencies can easily be seen without doing any algebra. A result known as the “low- Q Q Q approximation” states the poles should be located at about Q Q Q and 1 / Q 1/Q 1/ Q times the resonant frequency, or approximately 16.7 MHz and 150 MHz. Instead of a conjugate pole pair at the resonant frequency, the poles separate into a pair of real poles. When circuit elements are connected in parallel, the impedances combine as the inverse of reciprocal sums: Z = 1 1 / Z 1 + 1 / Z 2 + ⋯ = Z 1 ∣ ∣ Z 2 ∣ ∣ ⋯ Z = \frac Q ≈ 3 1 < 2 1 , so the circuit is said to be overdamped and it will not oscillate at all. It’s also easy to see how things change if we vary the values of the components. All of this can be read from the chart without doing calculations.
PRINTABLE SMITH CHART SERIES
The ratio of the characteristic impedance and series resistance means the Q Q Q of this circuit is about 3. The impedances cancel each other at this point, which would show as a sharp notch on the chart, except it is bounded below by the series 10 Ω resistor. Drawing the intersection of the inductance and capacitance lines shows the resonant frequency is 50 MHz, and characteristic impedance of this combination is a little over 30 Ω. For an example involving a resonant circuit, consider a series RLC circuit of a 100 pF capacitor, a 100 nH inductor, and a 10 Ω resistor. When the lines for a capacitor and inductor cross on the chart, the impedances are equal and opposite imaginary quantites, and the resulting sum is zero. While it is the case that “impedances add in series,” it’s only true when they are considered as complex numbers, so a little more care is required when looking at resonant circuits. frequency, with diagonal lines for the frequency-dependent impedance of capacitors and inductors. Reactance paper is a log-log chart of impedance vs. It permits quick, approximate characterization of passive networks.
PRINTABLE SMITH CHART SIMULATOR
Another method is to use a circuit simulator like LTSpice, which can produce exact results very quickly, but it also often obscures how individual components contribute to features in the graph.Ī third method used by engineers before the era of digital computers was specialty graph paper called reactance paper (or impedance paper).
One way is to derive a mathematical expression for the impedance or frequency response, but this becomes tedious and complicated, and it’s often no longer illuminating once more than 3 components are involved. In studying passive networks in electronics, it’s important to understand the frequency-dependent nature of components and how they interact when they are connected in series and parallel.
This page serves as a reference on the use of reactance paper, and some discussion of the process behind making the charts.
PRINTABLE SMITH CHART DOWNLOAD
They are free to download and use from Pen & Paper Nomographic. In 2021, I released printable PDFs of charts. Attention to typography and graphical precision were the driving motivation for making my own charts. I wanted them as a handy complement to computer simulation tools. In 2019, I began working on designing and printing nomographic charts useful in electrical engineering.
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