Q Factor or Quality Factor as q inductor is especially important in the event that a particular coil will be utilized to serve as an components of a filter that is selective. Quality is the proportion of the coil’s reactive (the composite portion of impedance) to its resistance (the real portion of impedance).

Q factor isn’t an absolute value, it changes in relation to frequency. The use of coils that are high quality can, for instance the creation of filtering systems that are distinguished by the steeper characteristics of transmission and consequently, better selection.

A typical dependence of coil’s q inductor coefficient on its frequency. A general trend is observed that coils with lower inductances have higher Q factor.

If inductance and capacitance are in series with regard to the source of power then we are talking about an resonant circuit in series. A real resonant circuit will have along with capacitance and inductance, certain amount of resistance called”the loss resistivity. It is comprised from the resistivity of the metal the coil’s core and the losses that are converted to resistance in the core of the coil and the losses converted to resistance in the capacitor as well as those of the wires connecting it. The lower the loss in resistance, the more efficient the resonant circuit. The main factor that decides what the performance of the resonance circuit is its quality. Quantity is defined as the proportion of capacitive or inductive resonance reactance to loss resistance.

The Q value of circuits is dependent solely upon its parameter. The quality factor of Resonant circuits can be found within the range of hundreds to several hundred. After proper transformations, we can get:

## Spiral inductor q factor

Spiral inductors make up one of the most popular passive components utilized in contemporary circuit designs. They are present in nearly every manufacturing technology that is used nowadays: integrated circuits made of silicon as well as RF and microwave integrated circuit (MMIC) technology of various varieties, multilayer module in organic or ceramic technology as well as most importantly printed circuit boards. They are utilized to serve a variety of purposes mostly used for biasing, filtering and shaping of signals. The engineer will typically want to select an inductor that has the highest possible performance for circuits which is compatible with other specifications of the manufacturing issue. The most commonly used figure-of-merit of inductors can be described as the quality, commonly called”Q” “Q”.

A figure of merit is helpful because it (hopefully) will give the designer an instant indication of the quality of the inductor that it will perform at the frequencies that are of interest. The more Q inductor is higher the higher the performance of the inductor. Q can be defined in many different ways, but all are in line with each other. The most basic description of physical Q in an asynchronously varying time harmonic system is:

Q inductor is not a dimension. The angular frequency of o. Q, which is the proportion of the energy stored by your system to energy dissipated which is multiplied with the frequency of the angular. Does this definition help the designer? If we look at an inductor as a simple model that includes reactive power, then the power of timing harmonics is proportional with the inductance. Thus, a higher power of reactive at a certain frequency is an “better” inductor. The power of the resistor comes from loss of the inside. The major losses in resistivity are caused by the inherently limited conductivity of conductors of the metal as well as the dielectric losses of surrounding materials. The resistance behavior is crucial for noise figures in RF circuits.

The majority of circuit designers prefer to employ definitions of Q that are based on the theory of circuit networks. They are of course in line to the definition of physical that was given earlier. For instance, for an uniport network, you can define Q by dividing the actual to the imaginary component of admittance.

There are other definitions that are feasible, for example, the two port definition of a network is possible.

How do you determine the quantum of a spiral inductor by using the electromagnetic (EM) simulator? From the first, it seems simple. First sketch the spiral along with the environment it is associated with. Next, add ports to the spiral. Thirdly run the spiral through the desired frequency and determine the Q value from the resultant S parameters. The issue lies in the fact that Q can be a highly sensitive measurement. There are numerous situations that EM simulations could go wrong. In the beginning of this article we review the most frequent pitfalls that could occur. To better understand what could happen, we look at both 3D simulators as well as planar simulators. The physical aspects of both simulators are similar, however, the implementation details for numerical simulation differ. The challenges are classified into three categories: accurately measuring resistances of the conductors; understanding the issues with ground return and ensuring that the ports are correctly calibrated. Additionally depending on the technology that is being employed, there may be additional issues. For instance, spiral simulations using silicon must be able to incorporate the thin silicon substrate.

In theory, 3D EM simulators are the most precise tool to simulate the spiral. The entire geometrical model is created by using tiny 3D cells. The electric field is determined for every cell. In the event that the mesh’s mesh size is precise enough it will allow the relevant physics to be recorded as well as the calculation of Q will also be taken into account. However, the mesh should be designed with care. Standard settings are not sufficient. The majority of these simulators don’t mesh the inside that is inside the inductor. Instead, they employ an imperceptible boundary that is applied to the metal’s surface and only mesh the outer areas to the metal. This can result in an incorrect estimation for the quality. The best method is to make sure that the metal is meshed inside.

This results in an extremely high number of cells of the grid. The mesh should be very fine when compared to the variations in the current flowing through the conductor. The current concentration is concentrated close to the conductor’s surface and decreases exponentially as you enter the metal. Additionally, the specifics of the current near the corners in the cross-section are crucial. The mesh size could be easily expanded by a factor of ten or more if the Q needs to be calculated accurately. So, a different method is recommended.

Planar EM simulators can be a well-known tool to simulate circuits. In these simulators the current problem is solved on the surface of conductors after the metal’s surface is mated. It is not necessary for meshing the complete spatial area of the problem, which also includes the dielectric regions that surround the inductor. The benefit is that planar simulations can analyze larger problems in comparison to 3D simulators. For instance the layouts of whole circuits are able to be studied dependent on the nature and complexity of the circuit. In reality, by limiting the problem to currents in the surfaces of the conductors, it can be difficult to find an exact answer to the Q of the spiral, due to similar reasons as the 3D simulators are not able to cope using an impedance boundary on the conductor’s surface.

This paper will present an approach to calculate the Q that doesn’t require meshing the inner part of conductors. Thus, planar simulators can be employed. (The method also permits 3D simulators with no meshing the inside of the conductors.) It is designed to model the inductor by using the boundary conditions for surface impedance that are typically available within EM simulators. Then, a second problem is modelled consisting of straight lines that have the same cross-sectional geometrical shape as that of the spiral. It is possible to determine the loss in linked lines can be calculated by with the help of cross sectional line modeling tools. In most cases it is a cross-sectional EM tool is used that incorporates the specific characteristics of the current distribution of the lines. The results from both the complete EM simulation and the cross sectional model are contrasted. The differences are employed to adjust the quality in the initial simulation. The method is based on the assumption that the spiral could be roughly modeled as straight line sections this is often the scenario. The edges of the spiral are typically a secondary factor when assessing the performance of the spiral. So designers can obtain an accurate estimate of Q without having to resort to ridiculous mesh density for 3D simulators. They is still able to use the planar simulator in case they want to.

What is it that makes Q an extremely sensitive measurement? In this article, we’ll explore a range of factors, starting with the primary focus of this paper: getting the conductor loss right. To illustrate the issue we examine an inductor spiral within an integrated circuit microwave (MMIC) procedure. Similar problems are also present in other technologies, including integrated inductors within package modules as well as silicon chip technology. It is common to MMIC technology. It is positioned on the GaAs substrate that is 100 millimeters thick. Gold lines are employed. The depth of the line measures around 3 millimeters. The lines are 10um wide and 6um wide gaps. The right side of this image shows the specifics of the mesh that is used for the programar simulator. The mesh’s size is 9500 undetermined.

The edges of the steel are joined. It is crucial that the simulator includes the non-zero conductivity of the lines because the distance between the turns on the spiral has in the same as the line’s thickness. This is typical for spiral inductors of all kinds including module, MMIC and silicon. The mesh density is typical for spirals. there’s multiple cells along the entire width of the line, and some cells on the vertical sides.

The figure above illustrates the two parameters of port S for the spiral that range from 0.1 through 10 GHz. Note that the simulation and experimental data are similar to what the human eye sees. In general, this kind of agreement is accepted by the designer who is using the spiral. It is also within the normal variation of the technology employed.

The results are noticeably different. The numerical simulation calculations differ from the numerical results with 27 percent when running in 5 GHz. This is common for Q calculations made using numerical simulators. The S parameter data appear to agree with each other, but the Q’s derived of the data quite different.

The issue lies in the fact that Q represents a ratio of reaction to resistance. The resistance is low at low frequencies and becomes greater as frequency increases. The calculation that calculates resistance may result in a tiny absolute error, however, it can have a huge relative error. If, for instance, you calculate the real resistance to be 0.1 Ohms at a given frequency and the mathematical calculations are 0.2 Ohms, the absolute error is 0.1 Ohms, which is an extremely small number to consider for designing circuits. The absolute error is 100 percent which results in a Q error of 50. Figure 4 illustrates the resistance in our example in which it is the true component of the impedance matrix that looks at port 1 when the port 2 has been shorted. There is a difference of 36 percent between the resistors in 5 GHz.

To be complete, we display the inductances for both the experimental and measured data.

The results are different by 19 percent when using 5 GHz. In general, numerical calculations of inductance are more in line with experimental data than the ones for resistance. The error in inductance is to the benefit of making the Q values be in line as they are less in the numerical data, which makes the Q smaller and resistance values are lower and the Q is therefore larger. There are many causes for the error in inductance. First, inductors possess external and internal inductance. Inductance is the proportion of the magnetic flux that flows through the surface to the current that creates an electromagnetic field. The magnetic field contribution within the conductors creates internal inductance, while magnetic fields outside of the conductors provide an external source of inductance. The significance of these two aspects is determined by the manufacturing technique and geometrical shape. A EM simulator must be able to calculate external inductance precisely since the measurement is dependent on the total flow of current through the conductors. This isn’t a particularly sensitive parameter in the context of mesh density. The internal inductance is much more difficult to determine precisely because the precise flow of current through the conductors has to be discovered.

Planar solvers employ an impedance-based boundary positioned at the conductor’s boundaries. The border condition relies upon approximations which break down near the edges of conductors. Based on the geometry of the conductor it is possible that the accuracy of the surface impedance method is to be questioned. Alternately, 3D simulators can use either impedance boundary conditions that are applied to the conductors’ surface or mesh the metal’s interior volume. But, this approach can cause inaccurate computation times due to the huge mesh needed for conductors. Thus, that the calculations of inductances within the spiral is subject to the same issues as finding the resistance of the conductor. Fortunately the internal inductance of the spiral is typically a small portion of the total inductance and the external inductance is dominant. If this were not the case it wouldn’t be an extremely efficient inductor.

The researchers are faced with the choice of either meshing the conductors’ interior using a small mesh by using the 3D EM simulator, or trying to apply the boundary condition of a surface in the planar simulator, and then risk getting an incorrect answer. This paper demonstrates how we can improve the surface impedance method so that we obtain a significantly more accurate estimation of Q while maintaining reasonable dimensions of the mesh as well as computational times.

To be complete, we will mention two other frequent issues with estimation of Q using EM simulators. Although they are not the primary subject of this article These other issues must be considered when analyzing Q. The first step is to discuss ground return. Inductance is only a unique concept in the event that the entire path of the current is understood including ground return. If not, it’s not possible to provide an exact answer to the magnetic flux that flows through the current loop since there is no complete current loop.

EM simulators make use of ports to stimulate the circuit and then analyze the S parameters that result. Every port has a concept of an local ground. The easiest way to find your local ground is consider the current. The current flows from the port and down the line. Where does it come from? It’s coming from port’s ground.

A wave port is depicted on the left of the image. The current flows down the line from the port. The return line is located situated on the outside of the port. This is where usually, a type of ground plane made of metal is utilized. The port to the left side is an inside circuit-type port, which is utilized in both 3D and planar simulators. This line gets cut, and the port is inserted. It is considered being a two-point probe that has its own internal impedance (usually around 50 Ohms). The probe tip in red is connected to one end. The current is pushed out of the port and onto the line. The opposite side is the ground that is used by the port.

The most popular kind of port that is used in the planar simulator. The left-hand side of the diagram illustrates an explicit grounding plan. A strap of metal is connected on the floor plane. It is clear there is a return voltage that is flowing upwards through to the strap that is grounding. On the right side, you can see an implicit grounding plan. The grounding strap is not present. The return current comes from the infinite in this case. The benefit of using an concrete grounding is that the engineer can tell exactly where the current originates from, but at the cost of more parasitics in the port because that of the strap for grounding. The implicit port is less parasitics, however care should be taken not to get mistaken for the ground return.

One of the most frequent issues that occur when simulations simulate spiral inductors is that the ground reference used in the simulation is not in line with the physical reality. For instance the on-chip spiral can be assessed with a probe on a wafer. The probe comes with an electrical contact as well as at least one ground contact. What do we determine the return path for the spiral mapped out within the device? Common scenarios include the drawing of a ground ring around the spiral, on the same layer of metal as that of the actual spiral, or using vias to move down into lower levels of metallization within the stackup, and then returning to some kind of ground nets or the ground plane. The designer has to ensure that EM simulation is as close to the real ground return to the greatest extent is possible.

Another issue with ports involves deembedding. Embedding a port into an EM simulator can resolve two issues. First, the parasites that are associated with the port are eliminated. In the example on the image on the left Deembedding eliminates the effect of these parasites in those S parameters. Then, deembedding establishes the reference plane of the port. It is the place where the incident wave from the port has a zero degrees of phase. Every port has reference planes; typically it is located at the port’s location until a deembedding distance is established. Embedding is the process of simulating canonical structures with the same configuration of ports as the port that was originally. The most frequently encountered issue for spirals lies in the fact that the plane that is used for the spiral within the circuit is not in agreement with the location of the reference plane that is used in an EM simulation.

In a spiral, the Q is dependent heavily on the loss of conductor. To calculate the loss of conductors requires the current distribution within the spiral is accurately calculated. However, the distribution needs to be more precise than it is for regular EM simulations. Conductor loss is normally an effect that is secondary in order to get accurate S parameters. This is why it is appropriate to take that loss in the conductor as an impedance boundary on the conductor’s surface. A rather coarse mesh may be applied to one side of conductor. For instance the mesh on the right-hand part of the figure 1 usually sufficient in S parameters calculations. A general guideline is that five or more cells along the line is a small enough size for a cell. Sometimes, lines with tight coupling in filter structures need an area of 1 seventh of the line. A mesh that is smaller than this can be a waste of computational resources and could result in numerical problems. (This is because the matrix is increasing as the number in the matrix condition is becoming larger as the cells get smaller.)

If we consider calculating Q, the standard assumption of simulations for conductor loss can be a source of trouble. The first is that surface impedance estimates require two key assumptions: the conductor’s cross-sectional dimension (height as well as width) are significant in comparison to the depth of the skin of the material, as well as there aren’t any nearby conductors that could affect the currents. The two assumptions above are not met when using the spiral topologies of conductors. In addition, the standard meshing density rules of five cells along the line is not sufficient to achieve the accuracy required to calculate Q. The problem of surface impedance can be solved with the help of the 3D EM simulator , and then meshing the conductors, however at a cost. The scope of the issue grows by a factor of ten. In the second section in this piece, we’ll examine each of these two issues in greater depth.

## How to measure q of inductor

The calculation of q factor is accomplished using bridge techniques or is based on the phenomenon of resonant voltage. In the real world it is typically measured indirectly using the 3 decibel frequency within the LC Resonant Circuit and then computing it using the formula:

where: F resonance is the The frequency at which circuits resonate, or the middle band of.

3 dB bandwidth Bandwidth (f2-f1) determined by the three decibel amplitude decrease to the 3 decibel amplitude drop.

**Reference:**

https://iviter.pl/encyklopedia/dobroc-ukladu/

https://www.am.szczecin.pl/uploads/faculties/wi/c02_2012_RLC.pdf

https://elektronikab2b.pl/technika/32369-elementy-indukcyjne-poradnik-konstruktora