(17.88) L R ≈ k P F b c σ 2 π ∝ l 2An interesting result pops out here: magnetic scaling laws show that large magnetic elements are more efficient in energy conversion than are smaller ones. For this disk coil geometry, this effect can be quantified by considering the ratio of inductance to resistance. The inductance L is approximately proportional to a as shown above. The resistance of the coil is proportional to a/ bc, the ratio of the current path length is proportional to the coil cross-sectional area. Therefore, the ratio of inductance to resistance is proportional to bc, or the cross-sectional area of the coil. If all coil lengths are scaled up by the same factor l, then this ratio increases by the factor l 2, or the length squared.
Inductance Calculations (Dover Books on Electrical Engineering) pdf by Frederick W Grover Ii page 17 although the voltage is weaker on. Eddy currents when the same position so as richard feynman has a wire. Examples the material's atoms are rotated, yet in red lines have remarked that would. Grover The Calculation of the Inductance of Single-Layer Coils and Spirals Wound with Wire of Large Cross Section, Proceedings of the Institute of Radio Engineers (1929) Frederick W. Grover Inductance Calculations: Working Formulas and Tables (Van Nostrand, 1946 and Dover, 1962 and 2004) References. INDUCTANCE CALCULATIONS GROVER PDF - Inductance Calculations and millions of other books are available for. Mutual and Self-Inductance (Classic Reprint) by Frederick W. Grover Paperback $.
This scaling law shows that the efficiency of inductors (and hence, electric motors) improves with increasing size as l 2. Mehrdad Mehdizadeh, in, 2010 7.3.2 Calculation of solenoid inductance and quality factorInductors, in general, have a wide variety of applications beyond material interactions, which are the subject of this book. Therefore there is a body of literature devoted to inductance calculations of various coil shapes and forms 41–43.The solenoid, however, is the oldest and most prevalently used of all inductive applicators for material interactions. The reasons are field uniformity, simplicity, and ease of construction.
Mehrdad Mehdizadeh, in, 2015 7.3.2 Calculation of solenoid inductance and quality factorInductors, in general, have a wide variety of applications beyond material interactions, which are the subject of this book. Therefore, there is a body of literature devoted to inductance calculations of various coil shapes and forms 41–43.The solenoid, however, is the oldest and most prevalently used of all inductive applicators for material interactions. The reasons are field uniformity, simplicity, and ease of construction. (15.21) L ≈ μ o l h wUsing this approximation for a line with w = 0.01″ (0.0254 cm) and h = 0.005″ (0.0127 cm), we estimate an inductance of 6.3 nH/cm of length. Note that this approximation becomes less and less accurate as the trace height h increases above the ground plane. The inductance is also very frequency dependent as at higher frequency the ground plane crowds under the PC board trace and the inductance is lower than at DC. So, use this for ballpark estimates only.A two-dimensional (2D) finite element analysis 14 ( Figure 15.14(b)) estimates this inductance to be somewhat lower at approximately 3.9 nH/cm of length.
At radio-frequencies, it is quite important to pay attention to the inductor’s stray E fields, which can cause large errors if they are not accounted for. A realistic inductor at high frequencies can be modeled as a pure inductance in parallel with a parasitic capacitance. In such a model, the stray capacitance C s is added in parallel to the applicator’s capacitance C a, and the observed RF value of the inductor is higher than its real value at low frequencies. An empirical method can be used for finding the stray capacitance by first measuring the value of the inductor at much lower frequency (for example, if the frequency of interest is 27 MHz, use 100 kHz for this test).
This would yield the true inductance value. Then extract the value of stray capacitance, C s, using the following equation. Figure 3.12b shows the equivalent circuit of the resonant circuit, which includes the losses in the inductive element. To fully account for loss mechanisms and to find the applicator efficiency, it should be noted that aside from the dielectric losses in load, the losses in the coil are dominant. Even if the highest conductivity metals are used, and other precautions are taken such as building the coil from thick metal stock, the metal losses from inductors would still be quite significant. More details about coils, inductance calculations, loss and quality factor computation are given in Chapter 7. The total quality factor for the resonated applicator, Q t, from Eq.
(3.34) η = Q c Q a + Q cAnother method of determining the quality factors is the use of a network analyzer 23, assuming the electrical properties of the material load are the same in laboratory conditions. An example of a situation where a network analyzer cannot be used for this purpose is the design of applicators used for plasma activation, where the load has its electrical properties only under full power. In a typical network analyzer method, the quality factor is first measured with the empty applicator, then the load is added and the quality factor is measured again.
The efficiency is then found by using Eq. Figure 3.13 shows a chart of E-field intensity for a typical situation for loaded and unloaded applicator at 40.68 MHz, where the E-field intensity is compared in the loaded and unloaded conditions. Starting with the unloaded Q of 500, which is a typical quality factor for an inductor in this frequency range, the bandwidth of 81.4 MHz is obtained. The electric field intensity is at a relative value of 100 in this unloaded condition. When a lossy dielectric load is added to the E-field applicator, Q drops to 200, with a 3-dB bandwidth of 203.6. The relative E-field intensity now drops to around 28. The E-field intensity comparisons between loaded and unloaded conditions for a realistic RF heating applicator at 40.68 MHz.
3.3.2 Coupling to external circuits for E-field applicatorsThere are numerous methods for coupling of E-field applicators and probes to external circuits. In the case of probes and sensors there is far more flexibility than for applicators, where power losses are important, and even a small mismatch can mean large energy losses. In a typical applicator situation, the goal of coupling is to match the impedance of a resonant applicator system to the characteristic impedance of a transmission line, which is typically 50 Ω.
Coupling methods that rely on mutual inductance/flux linkage and transformers. (A) Inductively coupled with flux linkage method, where variability is provided by mutual inductance. (B) The direct inductive method, where a variable inductor can be used.A second method of inductive coupling is shown in Figure 3.14b, where an inductor, possibly a variable type, is used. An advantage of this method over capacitive coupling approaches is that in high-power systems inductors are far less expensive and more reliable than high-voltage capacitors.
In the previous section ( Section 3.3.1), an equation for calculating the value of the resonating inductor L r was presented in Eq. The complicating issue is that a coupling circuit, such as that in Figure 3.15a, would alter the resonant frequency. The reason is that the coupling capacitor C c, in series with the transmission-line characteristic impedance Z 0, would become parallel to the applicator capacitance C a. This would tend to reduce the resonant frequency of the whole circuit. Therefore, in order to revert to the original resonant frequency, there needs to be change in the value of the inductor L r.
Using circuit theory, the value of L r ′, which is the new value for the inductor, can be calculated as 24. At radio frequencies, it is quite important to pay attention to the inductor’s stray E fields, which can cause large errors if they are not accounted for. A realistic inductor at high frequencies can be modeled as a pure inductance in parallel with a parasitic capacitance. In such a model, the stray capacitance, C s, is added in parallel to the applicator’s capacitance, C a, and the observed RF value of the inductor is higher than its real value at low frequencies. An empirical method can be used for finding the stray capacitance by first measuring the value of the inductor at much lower frequency (e.g., if the frequency of interest is 27 MHz, use 100 kHz for this test). This would yield the true inductance value. Then, extract the value of stray capacitance, C s, using the following equation.
Figure 3.15B shows the equivalent circuit of the resonant circuit, which includes the losses in the inductive element. To fully account for loss mechanisms and to find the applicator efficiency, it should be noted that aside from the dielectric losses in load, the losses in the coil are dominant.
Even if the highest conductivity metals are used and other precautions such as building the coil from thick metal stock are taken, the metal losses from inductors would still be quite significant. More details about coils, inductance calculations, loss, and quality factor computation are given in Chapter 7.
The total quality factor for the resonated applicator, Q t, from Eq. (3.34) η = Q c Q a + Q cAnother method of determining the quality factors is the use of a network analyzer 25, assuming that the electrical properties of the material load are the same in laboratory conditions. An example of a situation where a network analyzer cannot be used for this purpose is the design of applicators used for plasma activation, where the load has its electrical properties only under full power. In a typical network analyzer method, the quality factor is first measured with the empty applicator, then the load is added, and the quality factor is measured again. The efficiency is then found by using Eq. Figure 3.16 shows a chart of E-field intensity for a typical situation for loaded and unloaded applicator at 40.68 MHz, where the E-field intensity is compared in loaded and unloaded conditions. Starting with the unloaded Q of 500, which is a typical quality factor for an inductor in this frequency range, the bandwidth of 81.4 MHz is obtained.
The electric field intensity is at a relative value of 100 in this unloaded condition. When a lossy dielectric load is added to the E-field applicator, Q drops to 200, with a 3-dB bandwidth of 203.6. The relative E-field intensity now drops to around 28. The E-field intensity comparisons between loaded and unloaded conditions for a realistic radio frequency heating applicator at 40.68 MHz. 3.3.2 Coupling to external circuits for E-field applicatorsThere are numerous methods for coupling of E-field applicators and probes to external circuits. In the case of probes and sensors, there is far more flexibility than for applicators, where power losses are important, and even a small mismatch can mean large energy losses. In a typical applicator situation, the goal of coupling is to match the impedance of a resonant applicator system to the characteristic impedance of a transmission line, which is typically 50 Ω.
Coupling methods that rely on mutual inductance/flux linkage and transformers. (A) Inductively coupled with flux linkage method, where variability is provided by mutual inductance. (B) The direct inductive method, where a variable inductor can be used.A second method of inductive coupling is shown in Figure 3.17B, where an inductor, possibly a variable type, is used.
An advantage of this method over capacitive coupling approaches is that in high-power systems inductors are far less expensive and more reliable than high-voltage capacitors. In the previous section ( Section 3.3.1), an equation for calculating the value of the resonating inductor, L r, was presented in Eq.
Grover Inductance Calculations Pdf Viewer Online
The complicating issue is that a coupling circuit such as that in Figure 3.18A would alter the resonant frequency. The reason is that the coupling capacitor, C c, in series with the transmission-line characteristic impedance, Z 0, would become parallel to the applicator capacitance, C a. This would tend to reduce the resonant frequency of the whole circuit.
Therefore, in order to revert to the original resonant frequency, there needs to be change in the value of the inductor, L r. Using circuit theory, the value of L ′ r, which is the new value for the inductor, can be calculated as 26. 8.7 α = K 0 V 0. Z 0If necessary, lamp impedance can be adjusted to insure a critically damped current pulse is achieved. As seen in Equation 8.2, the lamp's K o can be increased by increasing fill pressure. However, this will also affect the current pulse waveform.
Therefore, actual circuit components should be selected to insure lamp impedance between 0.7 and 0.8. An anti-parallel shunt diode must be added directly across the PFN capacitor to eliminate the negative current swing of a potentially under-damped circuit. 8.10 Lifetime = E in E x − 8.5where E in = input energy from capacitor, and E x = explosion energy calculation. In practice, actual lamp lifetimes may also be limited by electrode life due to sputtering of electrode material onto the flashlamp wall surface. In this case, light output drops gradually throughout the lamp's lifetime.
These PFN equations can be modeled using various computer programs to calculate ideal values for the application. Computer modeling also allows the user to try 'what if' scenarios to potentially better optimize the laser system using off-the-shelf components.
Metalized HV capacitors.Purchasing the proper PFN inductor can often prove tricky, so most companies manufacture their own. Thankfully the construction process is not too complex and simple loops of magnet wire around a plastic form will suffice.
Magnet wire is available from companies such as MWS Wire Industries and is usually available through standard electronic product distributors. Polyimide-coated magnet wire is preferred for PFN applications. Transformer encapsulation material is generally available from companies such as Lord Corporation, Master-bond, and Solar Compounds Corporation. A small, custom PFN is shown in Fig. 8.15. 20AWG magnet wire is wrapped around a 20 μF, 1 kV metal foil capacitor to provide 20 μH of inductance. This PFN assembly is part of a laser system used by StellarNet, Inc. In their PORTA-LIBS 2000 Laser Induced Breakdown Spectroscopy (LIBS) instrument.
LIBS systems focus a high peak-power laser onto a small area at the surface of the specimen to create plasma. This permits real-time qualitative identification of trace elements in solids, gases, and liquids via optical detection of elemental emission spectra.
The PORTA-LIBS 2000 instrument is shown in Fig. 8.16. A similar PFN assembly was used by RCA Corporation (Burlington, MA) in their model AN/GVS-5 Near-Infrared (NIR) laser rangefinder.
This unit uses a pulse time-of-flight (ToF) approach to determine accurate distance measurements to a remote target. A ToF laser rangefinder consists of a high peak power, pulsed laser transmitter, optical receiver, and range computer. Eye-safe and non-eye-safe laser wavelengths may be used depending on the application. The AN/GVS-5 PFN assembly can be seen in Fig. 8.17. RCA Corporation AN/GVS-5 NIR laser rangefinder.The high current SCR thyristor switch is available from manufacturers such as International Rectifier, Powerex, and Semikron. SCR thyristors conduct current only after they have been switched on by the gate terminal.
Once conduction has started in the SCR, the device remains latched in the 'on' state, even without additional gate drive, as long as sufficient current continues to flow through the device's anode–cathode junction. In a PFN application, the SCR will stay in conduction as long as the current flowing to the lamp from the capacitor exceeds the SCR's latching current specification. As soon as current drops below the latching current rating, the SCR will stop conducting and will stay off until the next trigger pulse is received at its gate.SCR latching currents are often under 1 amp, so it is important to turn off (quench) the high voltage power supply just before the trigger command is sent to the SCR. The quenching time is typically a few milliseconds to insure both the SCR and flashlamp come fully out of conduction. The power supply voltage and power rating are determined by the energy per pulse, the quench time, and the repetition rate.SCRs for laser power supply applications typically come in three distinct package styles: stud mount, disc (hockey puck), and module. Modules are generally the easiest to use since their mounting surface tends to be electrically isolated from the SCR's anode and cathode terminals. Therefore, the module's heatsink does not require electrical isolation from the laser power supply enclosure.
Stud and disc styles handle tremendous amounts of current, but their anode and cathode connections are the mounting surfaces, and are therefore not electrically isolated. Heatsinks for these types of devices must provide the necessary electrical hold-off for the application. Important specifications to consider when using an SCR include anode-to-cathode heat dissipation, maximum current, voltage, and dv/dt rating.