3.2.3. Ferrite Loading
Magnetic ferrite loading can enhance a transmitting signal as high as 2 to 10 dB for MHz [Devore and Bohley, 1977]. There is an optimum frequency range where ferrite loading is beneficial. The ferrites are compound of iron and other magnetic materials.
Loaded loop antennas have been generally used as receiving antennas because of insufficient information about them in the literature as radiating elements.
Cylindrical cores are suitable for low frequency applications although spherical cores are primarily applicable for high frequency radiator [Islam, 1963]. One of the important limitations for ferrite antenna design is to provide selected ferrite material. Every ferrite material has its own limitations. Moreover, in practice, the selected materials cannot meet its specifications.
The ferrite loading invalidates “in phase assumption” of the loop current which is generally negligible in real applications. The ferrite (ferromagnetic) permeability can be considered as a constant number at distinct frequencies although it is frequency dependent in reality. This consideration gives a chance to model a ferrite loaded loop antenna (ferrite antenna) as a magnetic (elementary) dipole.
In order to increase the loop performance, a high permeable and low loss ferrite core (ceramics) can be inserted into the loop (ferrite loop) [Rumsey and Weeks, 1956], [Balanis, 1997]. Magnetic material loading of loop antennas ensures high magnetic flux. The low loss (high resistance) corresponds to small Eddy currents inside the ferrite. It is known that fields in the finite cylinder core are not uniform even in a uniform applied field. The ferrite loading makes the antenna more sensitive, but less stable and nonlinear in some cases such as high frequencies although the loop antenna (not loaded) is less sensitive, but more stable and linear. The loaded one shows up very high inductance and less capacitance for resonance behavior. To have low demagnetizations, as possible as thin structures should be used.
The performance improvement by ferrite loading means - increasing ,
- increasing of ratio, implicitly related to the input impedance . In order to increase
- the perimeter and/or the number of turns can be increased. This makes the complex current distribution and leads to more difficult analytical model.
- high permeable ferrite core/cores can be inserted into the loop (ferrite loop) [Balanis, 1997].
The loaded loop calculations are generally approximate because behavior of the ferrite loop is not easy to calculate except for special case of an ellipsoidal core [Rumsey and Weeks, 1954]. Therefore, experimental techniques with test dipoles such as a static measurement method were proposed for the rod type ferrite loop modeling [Steward, 1957]. In the experiments,
- the loops must be well-balanced (ground plane effect), - the experimental equipment must be well-shielded,
- the experimental area should be independent of surrounding ferrous/non-ferrous materials1.
In these measurements, a cross-wound coil and moderately distributed winding were investigated2. variation as a function of ferrite cross-sectional area, number of turns and number of ferrite rods were given.
The calibration was performed by a theoretically known single loop magnetic field [Steward, 1957].
In practice, rods are commonly used instead of a one-piece ferrite rod. This increases adjustment ability of the inductance and may also help to reduce heat effect. In addition, magnetically loaded loop antenna is electrically larger than the unloaded loop of a same size. Therefore, development of dimensional resonance effect (large standing waves) leading to high losses at high frequencies will be an issue. To avoid this effect,
1 In experiments, reasonable tolerance was observed for non-magnetic materials [Stewart, 1957].
2 It was also claimed that the typical ferrite loaded loops have little electrical advantage over air loops. The packaging advantage may be significant. For constant , can be decreased [Stewart, 1957].
the condition of must be satisfied where is the ferrite rod length and is the wavelength [Devore and Bohley, 1977].
Ferrite loaded loop antennas are popular due to their small sizes for the same performance3. The ferrite loading (rods) concentrate magnetics flux from a large area to a small area, therefore, reducing the antenna dimension. As an example, if an axis of a ferrite rod can be located parallel to the uniform ⃗⃗ (the rod length is much greater than the diameter), uniform magnetic field is distorted as shown in a following figure [Laurent and Carvalho, 1962].
Magnetic field degradation due to a ferrite rod loading.
Physical mechanism of the magnetic field concentration can be explained as follow: due to very high permeability of the ferrite rod, the ferrite reluctance4 is very low than the air reluctance against the magnetic field. Therefore, the large number of the field lines concentrates in the ferrite. In this case, the induced voltage of turns ferrite loaded antennas for the same diameter of rod and coils becomes
where is for the air-loop and is the effective ferrite load permeability. It is clear that the ferrite loading increases the induced voltage times more. This means that the coil area can be reduced times less for the same induced voltage. If the rod and coil have not same diameter, the formula becomes different [Laurent and Carvalho, 1962]. depends on
- the initial material permeability,
- the ratio of the rod length over the rod diameter, .
Although there are some formulas for , graphical results are also given for its and dependencies as below [Laurent and Carvalho, 1962].
In this figure, it is clear that the higher is the higher (the rod length must be much larger than the coil diameter). And, the coil length must also be much smaller than 5.
3 Effectiveness of an air-loop antenna decreases with its decrease in dimension.
4 The magnetic reluctance is inversely proportional to the magnetic permeability ( ).
5 Otherwise, a correction factor should be introduced as a function of the coil length to rod length due to accounting uncoupled field lines by the turns coil [Laurent and Carvalho, 1962].
Effective Coil Permeability, It depends on
- relative permeability (initial) of the ferrite material, - coil geometry,
- rod (ferrite) geometry.
Its dependencies are generally investigated by experimentally. For example, the behavior of as a function of is experimentally given at below [Laurent and Carvalho, 1962].
can also be related to and as
√
Effective Height,
The ferrite loop for the same diameter of rod and coils, it is
where is the effective height of the air loop antenna. If the rod and coil has not the same diameter, the formula becomes different as [Laurent and Carvalho, 1962]
[ ( )]
where linearly depends on , therefore, large one is desirable. However, depends on and (from second graphic), therefore, that large is desirable means that large is preferable for constant . As a result, maximum is good for the best and also for the best ratio.
Increasing ferrite rod cross section directly increases .
In fact, electric dipoles are short/shorter antennas in terms of their lengths versus a wavelength, but they are long in terms of length to diameter ratio. The cored loop antennas are relatively long in terms of length to width ratio. When the length to width ratio of the core is relatively large, increase in the core does not influence the way demagnetization concentrates external flux [Kaplan and Suissa, 1998].
Signal to Noise ratio
Consider an equivalent circuit of the ferrite antenna shown at below [Laurent and Carvalho, 1962].
An equivalent circuit of the ferrite antenna.
where and (total tuning capacitance) are the coil lumped parameters. is the load resistance. In this case for , the ratio and an equivalent noise voltage area
√
where √ . Therefore, . And, is the Boltzman’s constant, is the the temperature degrees Kelvin and is 3 dB bandwidth of the device. Then, the ratio for becomes
√ √
where is a modulation index and is a form factor. In this formula, the value of is not present that gives freedom to choose the value, consequently, the tuning capacitance required [Laurent and Carvalho, 1962].
The major factors to improve the ratio are , and . The inductance does not affect , directly.
According to the figures, there is a particular size of coil for best performance of gives maximum
.
Packaging Advantage
The ferrite loading gathers magnetic flux resulting larger effective loop area. Therefore, less wounding by wires becomes sufficient comparing with an air loop for a given sensitivity. This reduces the wire losses but adds the core losses (more temperature dependent). For comparable performance between the ferrite and the air loops, the length of the ferrite core should roughly be equal (economic) to the diameter of an equivalent air loop. This means that one dimensional size chancing is enough for the ferrite loop although two dimensions are necessary for the air loop.
3.2.3.1. Electromagnetic Modeling
Electromagnetic modeling of the ferrite loaded loops is rare and generally needs complex calculations.
One of the important complexities in this calculation comes from the end of cylindrical core.
Islam investigated a solution for this problem, but for an infinitely long cylindrical ferrite core. He used standard boundary conditions on the ferrite surface and assumed that the coil is small justifies uniform current density. He used a retarded vector potential formulation with a numerical integration of the corresponding integrals which are two parts corresponding to the loop only and ferrite core loading. The importance of the correctness of the surface current calculation and the integral convergence problems were discussed in detail. It was declared that the ferrite loading causes an additional reactance and increases [Islam, 1963].
In principle, the field inside the core (the core field) is
where is the winding field, is the ferrite core demagnetization factor. The winding field can be related to the unperturbed fields as
where is the winding length and is the winding demagnetization factor [Devore and Bohley, 1977]. The demagnetization factors were formulated in [Devore and Bohley, 1977], [Stratton, 1941].
Kaplan and Suissa strove to develop an analogy between wire antenna theory and cored search coil basing on the relation of emf and gap mmf (concept for magnetic sensors) concepts. Explanations about emission of small amount of flux from end (no flux predicted) of the rods were given basing on not negligible core diameters [Kaplan and Suissa, 1998].
Hysteresis Effect
In high power levels, ferrite saturation and ferrite nonlinearities must be scrutinized. They can lead third harmonic generation and high hysteresis effect (loss).
3.2.3.2. Circuit Modeling
An equivalent lumped circuit model of an electrically small multi-turn loop antenna was given by [Devore and Bohley, 1977]. Magnetic loading increases magnetic flux, thus inductance and voltage sensitivity of the loops.
Inductance
Considering summation of core and winding fields, becomes
[ ( )
]
where low loss core is negligible and long solenoid are assumed. Dimensions are in centimeters [Devore and Bohley, 1977].
Capacitance
In the presence of a ground plane and tuning capacitors, capacity to ground (or chasis) per turn and intern capacity must be taken into account for ferrite loading multiturn loop. Considering these capacitances, an equivalent circuit representation of the antenna was given with consideration of these capaciatnces [Devore and Bohley, 1977].
Energy Dissipation (Core Losses)
Ferrite loading adds core losses beside resistive losses of wiring. The core losses are frequency (also tempereature) dependent because is frequency dependent. They generally increase with frequencies below 100 MHz. Therefore, the efficiency calculation becomes a design issue. In order to account energy dissipation in the ferrite rod, can be considered as a complex number as
where is the classical inductance of the loaded ferrite, is
where is the effective series resistance for energy dissipation in the ferrite and can be given as
( )
[
] where dimensions are in centimeters [Devore and Bohley, 1977].
Skin Effect Loss Resistance
√
( )
where is the proximity effect [Smith, 1971], [Smith, 1972a].
Radiation Resistance : Ferrite Antenna as a Transmitter
of the loop can be represented as an alternative way for
(
) ( )
where at a distance is a design parameter and can be maximized by the ferrite loading. increases with ferrite cross sectional area, but with increasing the loop inductance. Increasing the length of the ferrite allows the distributed winding with greater extend leading to decrease is also effective to increase the
. However, increasing the ferrite cross sectional area is more effective. This parameter can also be used in the test measurements [Steward, 1957].
Alternatively, of the ferrite loaded loop can be represented as
[
]
where is relative permittivity of the core, is demagnetization factor. , and , are the geometrical parameters of the loaded loop. This formula can be factored as
where represents magnetic loading enhancement factor [Devore and Bohley, 1977].
Available Power : Ferrite Antenna as a Receiver
An equivalent circuit of a tuned and loaded ferrite antenna is shown in following figure [Pettengill et al, 1977].
An equivalent circuit of a tuned and loaded ferrite antenna.
The induced electromotive force (EMF) is
| ⃗ |
where is the ferrite relative permeability, is the EMF averaging factor. The load voltage is where , a quality factor of the loaded antenna is given as
where is a quality factor of the unloaded antenna. In this case, the load power is
and the available source power (matching with tuning)
| where 6 is the ferrite antenna inductance7
where is a factor depending on . Then, substituting and into
| ⃗ |
where the ratio can be maximized by optimum ratio close to unity. Experiments show that the ratio for a fully wound rod.
The effective ferrite rod permeability can be approximated as
⃗ ⃗⃗
where is the ferrite relative permeability. and are an effective permeability factor and a rod demagnetization (effective hysteresis) factor, respectively [Pettengill, 1977]. Here, ⃗⃗ shows the transmitted (Tx case) or received (Rx case) magnetic field. In a good design, is wanted to be independent from . To perform this, while , if one succeeds , then becomes independent from .
In practice, there are empirical formula for prediction of , is given for a range of as
( )
where can be maximized at a break point beyond which it does not increase with an increasing of ratio. This takes a place
√
6 More simply, where is the current [Devore and Bohley, 1977].
7 For , the inducance is where is the shape factor [Wheeler, 1947].
and it can be related with a formula of . Then, the available power for a fully wounded antenna rod of optimum ratio is [Pettengill et al., 1977]
| ⃗ | Moreover, minimum volume for a given ratio is
where is Boltzman costant, is absolute temperature, is receiver noise factor, is bandwidth and
√ [Pettengill et al., 1977]. In fact, exact prediction of the ferrite rod size is difficult due to non- linearities. However, roughly, larger diameter and larger length are good with high and low loss ferrites [Laurent and Carvalho, 1962].
Directivity
The ferrite antenna directivity can be calculated from where . A reception pattern is shown below. It is a directional pattern8 [Laurent and Carvalho, 1962].
Directional Omnidirectional
However, an omnidirectional pattern may also be desirable. In order to introduce this, two separate antennas are located at right angles with a phase shift of in one as shown above (at right) [Laurent and Carvalho, 1962].
Source Cancellation and Nulling the Field of Receive Loop
In fact, the ideal source cancellation is impossible. Therefore, a small portion of the source field (called
“free-air response”) is measured and stored as a function of frequency. Then, it is subtracted from the real measured data during the survey [Won, 2003]. Fundamental source cancelation techniques:
- Receiver-bucking: HEM sensor
- Transmitter-bucking: GEM-3 (40-60 dB gain in dynamic range: 100-10000 times reduction in primary field)
- Coil separation: For cancelling the primary fields.
Nulling the receive coil field with respect to the transmitter loop is a crucial technology for better detection of the objects. This can be performed by magnetically or electronically.
8 In many applications such as home receivers, the directional pattern is suitable.
- Magnetic Nulling
Keiswette et al proposed a multi-frequency GEM-3M system based on the creation of a magnetic zone by a transmit loop for a receive loop. The design of the magnetic zone needs a careful and precision calculation.
This was performed by a theoretical way based on a Legendre series expansion of the scalar magnetic potential satisfies Laplace equation [Keiswette et al, 1997].
- Electronic Nulling
Spatial Resolution
The spatial resolution of the coil is principally determined by - frequency,
- size of coil,
- coil distance from the source of magnetic field, - transfer function between the current source and coil.
It was shown that the spatial resolution be increased by decreasing the coil size and increasing the number of turns. This can be performed by an optimization process (apodization) such as winding coils using several (exponential) turns (each with a different radius) [Roth and Wikswo, 1990].
- Depth Relation with the Loop Size and Position
Depth range can be increased by increasing the size of the loop, but the spatial resolution is sacrificed.
Increased spatial resolution comes at the price of decreased depth (sensitivity). Smaller coils provide better resolution, but do not allow going more depth. It means that the detection range is strongly related to the coil dimension. Moreover, in the case of one detector, the detection depth varied by as much as % 30 depending on the tilt of the search head with respect to the shaft [Das and Toews, 1996].
Large Targets Close to the Coil and False Alarms
The coil has a sign-reversing region which is close to coil. Although this region is small in size generally, discrimination success of the large targets close to coil can be affected in this region according to being symmetric and non-symmetric.
Symmetric large targets generally can be coil’s positive or negative inducing area causes the signals and will be either positive or negative. It means that ferrous/non-ferrous assessment is to be the same in both regions.
Non-symmetric large targets generally can produce the biggest signal , but the smaller signal at the same location. This can cause reverse ferrous/non-ferrous sense (ferrous as non-ferrous / gold nugget as ferrous).
