# The importance (or not) of being resonant

 It is often that one hears in QSO, one OM to another, describing their antenna and stressing the importance of resonance, almost as qualification that if the antenna is resonant, then it performs well, and that by implication a non-resonant antenna has poor performance. Whilst the importance of resonance is often parroted on the bands, reputable texts do not seem to echo the sentiment. This article visits the meaning of resonance, and explores the variation in key system parameters for a nominal half wave centre fed dipole from about 15% below resonant frequency to about 15% above resonant frequency.

# Resonance

Before embarking on a discussion on the importance of resonance, resonance should be defined.

Resonance occurs when, at a frequency, energy is exchanged between two types of energy storage (eg kinetic and potential, magnetic field and electric field), and the total amount of energy stored remains constant through a complete exchange cycle. In an electrical network, that means that the equivalent two terminal network impedance has no net reactance, ie it is entirely resistive.

It might seem a little esoteric, but a broadband dummy load is not resonant at the frequencies where it is a good dummy load. It might exhibit resonance at extremely high frequencies, but at those frequencies where is it is a good broadband dummy load, there is negligible energy stored in electric or magnetic fields (compared to the energy dissipated in a cycle). So, whilst a circuit at resonance exhibits no net reactance at its terminals, zero reactance does not infer resonance in the general case (eg an ideal resistor).

The question raised is just what is resonant and where can it be observed? Is it the radiator, the feed line, or the entire antenna system as seen by the transmitter. If resonance is important, then surely we should be clear about what is resonant!

# Analysis

## Antenna System

The antenna system must be analysed as a complete system. In these models, it comprises:

• the feed line; and
• the ATU.

The analysis presented here is of a centre fed dipole either side of its fundamental resonance. The dipole is 21m in length of 2mm diameter copper in free space and modelled using NEC2 at a range of  200 frequencies every 10kHz from 6MHz to 8MHz. to determine the feed point impedance and antenna efficiency. The dipole length was chosen to be resonant at about 7MHz. The dipole is in free space to isolate it from the effects of ground image.

The antenna is then connected by 25m of feed line to an Antenna Tuning Unit (ATU) to transform the impedance of 50Ω to suit a transmitter. Most modern amateur transmitters are designed to deliver their rated output power into a 50+j0Ω load, and some will only develop their rated output power into such a load.

An ideal balun as appropriate to the feed configuration is assumed.

Three different types of feed line are modelled:

• 600Ω open wire line (150mm spacing, 2mm diameter copper, air spaced);
• RG58C/U 50Ω coax; and
• RG213 50Ω coax.

The ATU is an L network using practical values for loss of the L and C components. An L network is the lowest loss matching network, common T-tuner configurations will be slightly lossier. The ATU is used in the models to present the transmitter with a uniform load at all frequencies.

### Feed point impedance

The feed point impedance is a property of the radiator and is not affected by other (properly isolated) parts of the antenna system (feed line, ATU).

It can be seen from Fig 1 that the equivalent series reactance varies from about -240Ω at 6MHz to about 230Ω at 8MHz, and is zero at 7MHz (ie resonant). The equivalent series resistance varies from 48Ω to 110Ω over that range, and is 73Ω at 7MHz.

Feed point equivalent series reactance changes smoothly passing through resonance, and does not exhibit any sudden variation associated with resonance.

Feed point equivalent series resistance changes over the range in frequencies, and does not exhibit any significant variation associated with resonance.

The pattern is a property of the radiator and is not affected by other parts of the antenna system (feed line, ATU).

The gain pattern depends on the current distribution on the antenna wire. All power delivered to the feed point, and that is not lost in wire losses, will be radiated. Note that in Fig 3, at 8MHz the broadside gain is 0.25dB higher that in Fig 2 at 6MHz, but the main lobe in Fig 3 is narrower. At 8MHz, the Directivity is higher, and the losses are lower, so the gain is higher, but mostly at the expense of reduced field strength away from broadside direction.

Gain of a lossless dipole alone varies insignificantly over the range in frequencies, and does not exhibit any significant variation associated with resonance.

### Antenna wire loss

The antenna wire loss is a property of the radiator and is not affected by other parts of the antenna system (feed line, ATU).

Any conductor has resistance, and if current flows in that conductor, energy will be lost as heat. The antenna conductor is no different, and although the resistance varies with frequency (by skin effect, resistance is proportional to the square root of frequency in this case), and the current varies in amplitude along the length of the wire, it is relatively easy to calculate the energy lost due to heating of the conductor. Fig 4 shows the loss in energy due to heating of the conductor by the current (P=I^2*R). The loss in this case is insignificant, being less than 0.09dB or 2% of power over the 6MHz to 8MHz range.

Note that there is no significant variation in copper loss around resonance, the loss steadily decreases with frequency due to the influence of three factors:

• for a constant power radiated, the current in the antenna decreases with frequency, meaning an increase in radiation resistance (which is most of the resistance shown in Fig 1);
• the current distribution changes;
• the resistance per unit length of the conductor increases with the square root of frequency.

Loss in the antenna conductor is insignificant over the range in frequencies, and does not exhibit any significant variation associated with resonance.

## Feed line

Feed line loss will be different for each of the three modelled feed line types.

### 600Ω open wire line

Figure 5 is a plot of the three components of antenna system loss:

• copper losses in the antenna wire or radiator loss;
• losses in the transmission line; and
• losses the the ATU.

The total of all losses in this configuration is less than 0.5dB over the frequency range, 90% of the transmitter rated power into a 50Ω load is being radiated.

Total loss varies insignificantly over the range in frequencies, and does not exhibit any significant variation associated with resonance.

### RG58C/U 50Ω coax

Figure 6 is a plot of the three components of antenna system loss:

• copper losses in the antenna wire or radiator loss;
• losses in the transmission line; and
• losses the the ATU.

The total of all losses in this configuration varies significantly over the frequency range, from as little as 1.2dB near resonance to over 6dB at 6MHz. The tuner losses and the radiator loss are, as in the previous example, quite low and very acceptable. The line loss is the dominant cause of loss, and is least near resonance. The losses, even near resonance are not acceptable, this is not an efficient antenna system configuration, at best 75% of the transmitter rated power into a 50Ω load is being radiated.

Total loss varies significantly over the range in frequencies, and is best near resonance, but unacceptable.

### RG213 50Ω coax.

Figure 7 is a plot of the three components of antenna system loss:

• copper losses in the antenna wire or radiator loss;
• losses in the transmission line; and
• losses the the ATU.

The total of all losses in this configuration varies significantly over the frequency range, from as little as 0.6dB near resonance to 3.7dB at 6MHz. The tuner losses and the radiator loss are, as in the previous example, quite low and very acceptable. The line loss is the dominant cause of loss, and is least near resonance. The losses from 6.67MHz to 7.41MHz are acceptable, at best 88% of the transmitter rated power into a 50Ω load is being radiated, and over a 740kHz bandwidth, 80% of the transmitter rated power into a 50Ω load is being radiated.

Total loss varies significantly over the range in frequencies, and is acceptable within +/- 350kHz of resonance. There is no significant variation near resonance.

## Antenna Tuning Unit

The models use a L network tuner, with capacitor Q assumed to be 2000, and inductor Q assumed to be 100 at 1MHz and proportional to square root of frequency (eg Q=264 at 7MHz).

The popular T network tuner will have higher losses than an equivalent L tuner, but since tuner losses are so low in these models, the additional loss of a practical T tuner is insignificant.

ATU loss depends on the feed line configuration and varies over the range in frequencies, and is quite low, there is no significant variation near resonance.

# Further examples in brief

## High performance non resonant antenna systems

### No-tuner matched dipole

A dipole for the 40m band, 20m above ground, cut just under a half wave at 20.28m long for a feed point impedance of 69.2-j37.0Ω (in this case), and fed with exactly 17.9m of RG6 (in this case) to transform the impedance to exactly 50+j0Ω (no ATU required), and then 7.1m of RG213 to make up the 25m length of feed line. The dipole is operated about 160kHz below resonance. The RG6 feed line operates with a VSWR of about 1.5 for a total RG6 line loss of 0.49dB plus 0.11dB for the RG213 for a total of 0.6dB. The RG6 is cheaper and lighter than RG213, and the loss is similar to the RG213 configuration described above. In this configuration 85% of the transmitter output power is radiated.

### Extended Double Zepp

The so called Extended Double Zepp (EDZ) is grand name for a centre fed dipole of about 1.25λ at the design frequency, and is popular because of its broadside gain. It is not resonant, the dipole is operated midway between the first parallel resonance and the second series resonance, and it is highly reactive at the feed point, presenting around 190-j900Ω for an EDZ on 7.1MHz 20m above real ground. A feed line of 25m of 600Ω open wire line and tuner will have losses around 0.4dB, so it is a very efficient configuration with moderate gain, 90% of the transmitter power is radiated.

### Five-eighth wave vertical

A five-eighth wave vertical is well known for its excellent performance, having high gain at low radiation angle with an omni pattern in azimuth. It is not resonant, the vertical is operated midway between the first parallel resonance and the second series resonance, and it is highly reactive when fed at the base. Nominally five-eights wave verticals are commonly used for mobile operation on the 2m band where, lengthened slightly to about 0.68λ, they have a base feed point impedance over a perfect ground of 50-j108Ω and will use a series tuning coil of around 0.1μH to offset the high capacitive reactance of the non resonant radiator element and using 50Ω coax, provide an excellent load to a transmitter.

## Poor performance resonant antenna systems

### Full wave dipole

Take a 7MHz half wave dipole 20m above ground, and operate it at its next resonant frequency of 14MHz, where its feed point impedance is 4800+j0Ω, and loss in 25m of RG213 feed line is 9dB. About 87% of the transmitter power is lost in the feed line.

### Full wave loop

Take a 7MHz full wave loop 20m above ground, where its feed point impedance is about 120+j0Ω, and loss in 25m of RG58C/U feed line is 1.4dB. About 30% of the transmitter power is lost in the system losses. (RG213 in this application would results in a barely acceptable solution with 1dB of loss.)

The examples demonstrate that there is no substitute for understanding how the components of an antenna system work together and designing a system solution that best meets a sensible set of design criteria.

# Summary

Fig 8 summarises the total loss of each configuration over the frequency range. With the open wire line configuration, performance is near independent of frequency, whereas with the coax lines, performance degrades more than 300kHz from the resonant frequency, and the RG58C/U configuration is unacceptable an any frequency.

The principle contribution to poor performance is operation of a lossy transmission line at medium to high VSWR. By contrast the low loss open wire line is operated with excellent performance at high VSWR.

Fig 9 shows the VSWR for each configuration. Note the high VSWR of the high performance solution using open wire line (G600).

Note that the VSWR curve for RG58C/U looks deceptively better. That is the result of measuring VSWR at the ATU end of the line, where line loss masks the extent of the mismatch.

VSWR, by itself, does not give a good perspective of performance.

Fig 10 shows the impedance looking into the RG213 line from the ATU. Note that at all frequencies in the range, there is significant positive reactance, the input impedance to the feed line / antenna combination is not resonant anywhere between 6MHz and 8MHz. What does resonance of the radiator element mean to the transmitter that might otherwise connect directly at this point?

Measurement of input impedance to the transmission line, by itself, does not give a good perspective of performance.

Table 1 sets out the key findings of the analysis of these three configurations. Note that the finding do not necessarily apply in general, but they do apply to the scenario of a half wave dipole near its fundamental resonance.

 1 Feed point equivalent series reactance changes smoothly passing through resonance, and does not exhibit any sudden variation associated with resonance. 2 Feed point equivalent series resistance changes with frequency, and does not exhibit any significant variation associated with resonance. 3 Loss in the antenna conductor is insignificant, and does not exhibit any significant variation associated with resonance. 4 The gain pattern changes smoothly passing through resonance, and does not exhibit any significant variation associated with resonance. 5 Loss in feed line can be significant, and is the main contributor to poor performance where it occurs. Feed line loss is cause by a combination of: length of the feed line; a feed line type with high attenuation per unit length under matched line conditions; and exacerbated by operation at relatively high VSWR Though the poor performing configurations perform best around resonance, the feed point impedance is very reactive (load angle greater than 45º) before much degradation. 6 ATU loss depends on the feed line configuration and varies over the range in frequencies, and is quite low, there is no significant variation near resonance. 7 VSWR, by itself, does not give a good perspective of performance. 8 Measurement of input impedance to the transmission line, by itself, does not give a good perspective of performance. 9 There is no substitute for understanding how the components of an antenna system work together and designing a system solution that best meets a sensible set of design criteria.

In summary, an antenna doesn't need to be exactly, or approximately resonant to perform well, but some lossy feed arrangements may depend on near resonance of the radiator to contain total system loss and so achieve acceptable performance.

# Glossary

 Term Meaning ATU Antenna Tuning Unit - a network for transforming impedance dB decibel decibel a power ratio expressed as 10*log(P1/P2) Directivity The ratio of the intensity of the radiated field radiated in the main lobe compared to the average of radiated field in all directions Gain Directivity - Loss (all in dB) VSWR Voltage Standing Wave Ratio