# EH ANTENNA THEORY

## Ted Hart

INTRODUCTION: The EH Antenna is a unique concept that allows the design of high efficiency broad band antennas that happen to be small. This document was prepared to briefly explain the concept.

EQUIVALENT CIRCUIT: Figure 1 displays the effective equivalent circuit of the radiating portion of an antenna (any antenna), which is simply a capacitor in series with the radiation resistance.

The instantaneous bandwidth of the simplified antenna (an equivalent series circuit) is related to the amount of capacity and the radiation resistance. The relationship is defined as BW=2RF2C where BW is the instantaneous +/- 3 dB bandwidth, R is the Radiation Resistance plus loss resistance in the other components of the antenna, F is the operating frequency, and C is the antenna capacity. It is obvious from the equation that an increase in resistance or capacity will increase the bandwidth. For this reason the EH Antenna uses large cylinders rather than thin wires and a unique configuration of developing the E and H fields to enhance the resistance.The large cylinders allow the antenna to be small.

To be able to pass current through the radiation resistance it is necessary to cancel the reactance of the capacitor. This may be done by adding a series inductance having the same value of reactance at the desired operating frequency. Now we have a series resonant circuit as shown in Figure 2. For maximum performance we can tap the inductor (coil) to provide a convenient 50 ohm match to allow use of a coax transmission line. The complete antenna is depicted in Figure 3.

Note that a variable capacitor has been added. This allows the antenna to be tuned over a small frequency range without significantly changing the performance parameters. However, any shunt capacity in parallel with the antenna capacity will reduce the bandwidth of the antenna and will affect the matching..

Note also that a source capacitor is placed in series with the feed line. At the operating frequency the resistive component of the input impedance of the antenna will be a maximum. However, there will be an inductive reactance in series with the resistance which must be cancelled to allow zero reactance to occur at the same frequency as maximum resistance. This allows the tap on the tuning coil to be set for a virtually perfect VSWR match.

INPUT IMPEDANCE: To illustrate the impedance of the antenna as a function of frequency, Figure 4 is a plot of input resistance, reactance, and VSWR x 10 for a typical EH Antenna. This was taken from a set of equations written to define the antenna. Measurements of the completed antenna provide similar characteristics. Notice that, unlike a conventional antenna, the resistance peaks at the operating frequency. The reactive component of the input impedance goes through 0 at the design frequency if the source capacitor is properly chosen. Due to the changing values of real and reactive components, VSWR also changes as a function of frequency. Note that the 2:1 VSWR bandwidth is about 62 KHz and the +/- 3 dB bandwidth is approximately 168 KHz. This antenna has an equivalent Q = 7000/168=41. The bandwidth would increase if the antenna diameter were increased.

The 7 MHz antenna in the example has a diameter of 2.36 inches and a length of 2.5 feet. A conventional dipole at this frequency would have a length of 69 feet. The efficiency of this antenna, which is typical of all EH Antennas, is very high, yet the total length of the antenna is only 1.8% of a wavelength, as compared to a standard dipole with a length of 50 % of a wavelength. How is this possible?

RADIATION ELEMENTS: To understand the concept of the EH antenna, it is necessary to look at the Electric (E) and Magnetic (H) fields of the antenna as shown in Figure 4. It is important to realize that the total length of the antenna is a small fraction of a wavelength. For this reason the cylinders are capacitors with negligible inductance.

When a high voltage is applied between the two antenna elements (cylinders) an E field is developed. The voltage is high at the feed point but must be zero at the end of the elements. Therefore, there is a large voltage difference between the two ends of each cylinder. That differential voltage causes a current to flow on the cylinders. In turn, that current causes a magnetic (H) field to surround the cylinders. Now we have the necessary ingredients to develop radiation, which include the E and H fields being physically orthogonal. They must also be in time phase. This naturally occurs because the H field is created by the E field. In other words, while the RF voltage is present (an alternating sine wave) conduction current flows on the cylinder and that current creates the H field.

Note that the E and H fields are contained within a sphere defined to have a diameter the same as the antenna length, and there are no reactive fields. This is in contrast to conventional antennas having large reactive fields extending to about 1/3 of a wav elength from the antenna where they are sufficiently large to combine and produce radiation. If you run the numbers you will find that the EH Antenna fields are reduced about 30 dB below a conventional antenna. These unique features are readily discerned from the information presented below.

INTEGRATED CONCEPT: Figure 5 combines Figures 3 and 4 to provide a clear picture of the process inherent to the EH Antenna. By way of explanation, the process begins with power (P=IV) applied to the antenna at point A. At point B the current is delayed 90 degrees relative to the voltage because the current passed through the inductor. Therefore, we could say that the power (P=jIV) is reactive at point B. However, at point C it is terminated in a load that is a capacitor, thus the current and voltage are in phase at the resonant frequency. The current through a capacitor leads the voltage which causes the power at point D to be real power. In other words, the current lagged through the inductor and leads through the capacitor, for a total of 0 degrees phase shift relative to the source. Current through the capacitor is displacement current, compared to conduction current on the cylinders.

The resonant circuit develops maximum voltage across the capacitor/resistor combination and that voltage is applied to the cylinders. We have already explained that the applied voltage creates an E field which produces a differential voltage which develops a conduction current on the cylinders which in turn develops the H field. The radiation resistance is developed as a relationship between the E field (volts per meter) and the H field (ampere turns per meter). The relationship between the two must match the impedance of free space, which is 377 ohms. The antenna can be thought of as a transducer that transforms the power applied to the radiation resistance to radiation in free space. In reality the radiation resistance is only a mathematical convenience to express the fact that power applied to the antenna is radiated, and the percentage of radiated power is related to the relative magnitudes of loss resistance and radiation resistance.

RECEIVING ANTENNA: The process described above is linear and reciprocal. Therefore, as a receiving antenna, a radiated signal (containing both an E and H field) impinges on the cylinders and produces a voltage across the capacitor/resistor which in turn produces power into a receiver connected to the antenna system. The unique design of the miniature EH Antenna allows sufficient receive power to be captured from radiated signals to exceed those captured by full size conventional antennas.

If the antenna is in the presence of noise, defined as either an independent electric or magnetic field, the antenna cylinders are short compared to a conventional antenna, and therefore create very little voltage. In addition, because the fields are independent, the radiation resistance is virtually zero. For these reasons the EH Antenna provides a very significant signal/noise enhancement when located in a noisy area.

EFFICIENCY: The efficiency of an EH Antenna may be readily determined by measuring the bandwidth at the operating frequency. From the basic definitions of a series resonant circuit; Q=XL/R=F/BW where Q is non dimensional, XL is the reactance of the tuning coil, R is the radiation resistance + loss resistance, F is the operating frequency, and BW is the instantaneous +/- 3 dB bandwidth. From these relationships we find that R= XL*BW/F. We can readily measure BW and F, and the following equation allows accurate determination of the capacity between the cylinders: C=0.546*L/D*D+2.05*D where L is the length of one cylinder and D is the cylinder diameter. Typically, an EH Antenna is specified to have a length to diameter ratio (L/D) and a diameter, measured in inches, which are the two parameters that control the bandwidth. Although we can accurately calculate the capacity of the cylinders, it is also important to know the stray capacity and the value of a variable tuning capacitor, if one is used. This allows calculation of the inductance of the tuning coil. Even with out a tuning capacitor the stray capacity can be large.

With that value and an estimated value of the loss resistance in the tuning coil the efficiency can be determined. It is simply the power radiated divided by the input power. The difference between the input power and radiated power is the amount of heat developed in the tuning coil. This is typically expressed as the efficiency =RR/(RR+RL) where RR is the radiation resistance and RL is the loss resistance. However, because we measure (RR+RL) we can write = (RM-RL)/ RM where RM is the measured value of resistance. Typically the efficiency is greater than 95%. For example, assume the measured resistance is 86 ohms and the loss resistance is 2 ohms. This gives (86-2)/86 = 97.7%, which is a reduction in efficiency equal to -0.1 dB. In an EH Antenna the only loss is in the tuning coil. We can estimate that loss by assuming a coil Q and the inductance is known, therefore R=XL/Q.

Stray capacity is primarily from two (2) sources. The major one is the self capacity of the tuning coil. The other is the capacity between the antenna and ground, where ground may be the coax shield or the tower on which the antenna is mounted or another item in close proximity.