The bandwidth limit of a small dipole antenna matching circuit

If we model the antenna as an RC circuits, no matter how sophisticated the matching circuits is, the best bandwidth we can get is given by the formula :

T is gain and R is the real component of antenna impedance and C is the equivalence input capacitance of antenna. This equation suggest that the larger the real component of the antenna impedance, the better bandwidth we can get. And the Larger capacitance, the better bandwidth we can get.

REFERENCE

V. Iyer , S. N. Makarov , D. D. Harty , F. Nekoogar and R. Ludwig  "A lumped circuit for wideband impedancematching of a non-resonant, short dipole or monopole antenna",  IEEE Trans. AntennasPropag.,  vol. 58,  no. 1,  pp.18 -26 2010 

Short dipole antenna impedance model (Python code)

from math import log
from numpy import pi, tan
from numpy.polynomial.polynomial import polyval


# Short dipole antenna impedance model

f = 27e6             # frequency
La = 1.4             # total dipole length
Dia = 0.001          # diameter of the conductor

wavelen = 3e8/f
k = 2*pi/wavelen     # wave number
z = k*La/2;
R = polyval(z, [-0.4787, 7.3246, 0.3963, 15.6131])
X = polyval(z, [-0.4456, 17.00826, -8.6793, 9.6031])
IM = 120*(log(La/Dia)-1.0) * 1.0/tan(z) - X

print  'Real:', R, ' Imag:', IM

Matching network design by random guess

Read an article named "A Lumped Circuit for Wideband Impedance Matching of a Non-Resonant, Short Dipole or Monopole Antenna", this article suggested a 5-elements wideband matching network with some both low pass and high pass sections and so it say it's a wideband matching network.

Then I trying to apply this circuit to 27.0MHz band, and a python code is made to randomly guess the 5 component values and evaluate the performance by calculating the reflection coefficient at 5 frequency point around 27.0MHz. After millions cycles of guess, this is the best result I can get.

L1 : 4.04e-06

L2 : 2.918e-07

C1 : 2.247e-11

L3 : 7.131e-07

C2 : 2.312e-11

These value is put into Agilent ADS to verify. With reflection magnitude plot and smith chart plot.

The green plot is the baseline reference matching result using simple 1-element matching and the blue plot is from the 5-element. The 5-element matching network appeared having a wider bandwidth compare to that of 1-element network. 

Promising.

Impedance matching bandwidth simulation test

Cascaded L-section matching network between 50 ohm source and 25 ohm load, @ 27.0MHz, using 1 L-section, 2 L-sections and 3 L-sections, all of the three configuration would matching perfectly at exactly one frequency point, that is 27.0MHz. However in many case we want good matching on a wider bandwidth. The question is, can a 3-section matching network works better than a single L-section?

Well, from the frequency response plot and reflection plot, we can see the bandwidth of 3-section network is not significantly wider than that of the single section.

Some other matching network topology need to be investigate to achieve the goal of broadband matching.

27MHz monopole antenna impedance measurement

500mm long AWG28 wire antenna, in serial with variable inductor, for matching.

Return loss in Smith chart plot, from 10MHz to 40MHz, at 28MHz, only real component remain.

Return loss in log magnitude plot, dip around 28MHz, quite narrow band, look like not very good.

Return loss phase plot

Stirling engine

For these few months, I suddenly want to put down RF things for a while and make a pure mechanical design project, so I made something like this.

The Stirling engine, is a type of external combustion engine, turns heat energy into kinetic energy, in the engine, working gas is being push back and forth between hot zone and cold zone, produce work done by expanding and compressing.

With many failed version before this, it finally could overcome friction and sustain movement. Key points is not to make alpha-type Stirling engine when you are a beginner, because it just requires high temperature different to run, and in component level, the piston have to be accurate to ~0.03mm for air-tight, have to be dry, clean, moisture-free.

This model takes one candle to power and it could not generate enough power to drive anything, anyway it still looks enough fun and it gives a lots of satisfaction when first time see it moves.

27MHz PLL + Modulator in construction