This tool calculates the inductance of a common object in electrical engineering: two parallel wires. This tool is designed to calculate the inductance of a coil of wire given the length of the coil, the number of turns, the loop radius, and the permeability of the core material. The inductance of a wire loop is a common textbook example of a circuit with inductance. Wire Inductance. A sample 14 turns, half radius of 3 inches and a width of 12 inches yield an inductance of. Inductance is the ability to store energy in a magnetic field, and coils are a common way to create inductance. Flat Spiral Coil: The inductance of a flat spiral coil can be determined by entering its dimensions in the boxes above. For coil inductance in Henrys: L = N 2 * µ * A / Cl. Microstrip Inductor Calculator. μr μ r = relative permeability. So in this text the inductance L is usually a given quantity. 68 × 10^(-8) Ω × m . Some of them were designed to be used in static solid-state NMR probes operating at 1 H frequencies of 300 and 600 MHz, see Solenoid 1–5 in Table 1, which were tested with a inductance measurement circuit []. , move the windings), so instead the coil. The microstrip is a very simple yet useful way to create a transmission line with a PCB. Inductance is a property of an electrical circuit that describes the amount of energy stored in the magnetic field created by the current flowing through the circuit. The auto-inductance of a coil is dependent on the mutual inductance between each current turn, the self-inductance of the coil’s wire, and the environment surrounding it. The capacitance calculated using this tool is the capacitance between a flat conductor and the ground plane over the conductor length. D D = diameter of the wire. The inductance of the inductor is calculated by the following empirical formula: where: L – inductance of meander (µH) N – number of turns; a – length of a lead (mm) h – height of the meander (mm) d – width. Current range is from 11 A to 60 A. In all cases, the current is assumed to flow in the outer surface of the conductors. Mutual Inductance. The secondary inductance indicated from the flat spiral coil calculator in Part 1 of the design was (2 x 71. The mutual partial inductance is calculated as mutual inductance be-tween two filaments and provides exact values [1]. In electrical engineering, the word bifilar describes wire which is made of two filaments or strands. The inductance for the two wire inductance might be useful in measuring the inductance for a signal and ground on a ribbon cable. A rectangle loop inductance calculator is a tool used to calculate the inductance of a rectangular loop of wire. 375 uH to 3. 5, we can see the significance of the earlier description of mutual inductance (M) as a geometric quantity. OF TURNS = 10 OUTPUTS: INDUCTANCE = 10. kL: field non-uniformity correction factor according to Lundin. Grover in 1946. The following is a design tool which calculates the inductance of an air core inductor. W. |. Z = Impedance in ohms. 2. 6 Band Resistor. Lastly, to calculate the inductance, use the following formula – L = R x sqrt (3) / (2 * pi * f). Coax Inductance Description. N: number of turns. Additionally, since the inductance is dependent upon its material surrounding, use Table-4 to determine an appropriate "K" factor (multiplier) for the inductance. Wire Microstrip Impedance. However, the twisted. Use the formula C = ε · A/d to find the capacitance C. Single layer air core inductor calculator. Conductor is assumed to have zero thickness and to have uniform height above ground. Round wire corrections are not required for single turn coils. Inductance Calculator. Figure 14. A is the cross-sectional area of the coil in square meters (m 2)L = √ [(L 1 *Sin(X)) 2 + (L 2 *cos(X)) 2] - aggregate inductance of coil Inductance in µH, dimensions in inches. H H = height of the wire above the plane. 47. Calculates the dc Resistance of a single rectangular cross section strip (or track/trace) of common conducting materials using the equation below. The formula for calculating the self-capacitance of an air-core single-layer solenoid is: Where. The use of a magnetic core is ineffective. Choose units for a and W. This calculator takes into account your fixturing length, cable length, and the presence of shields and will return an estimate of the capacitance a test will see from one wire to all other wires in the cable under test. to D. Another advantage of ribbon over round wire bonding is the better mechanical loop stability of ribbon bonds which can achieve lower loop angles and lower loop heights than round wire bonds. L (uH) = r^2 * N^2 / (8 * r + 11 * w) L = Inductance µH. The short answer is yes. Discrete Structures: z Wire Inductance Calculator z Strap Inductance Calculator z Air Core Solenoid. 36µH) and 3S (290. Parallel Wire Inductance Calculator. This formula applies at 'low' frequencies (<30MHz) ) using enameled copper wire. Broadside coupled traces are on adjacent planes and the return is identical to the trace in width and length. Coplanar Waveguide With Ground Calculator. Inductive Reactance/Admittance. Single layer inductor calculator. To actually make the coil, [Drew] recommends some means of magnification, and a supply of CA glue. The intensity B of the magnetic field of a solenoid composed of coils wound in air (that is, without a ferromagnetic core) can be calculated using the following formula: where: μ 0 = 4Π x 10 -7 H/m is the magnetic constant (vacuum permeability) N is the number of turns. Loop length and width must be greater than the wire diameter. wire inductance L int = µ 0/8π, and the resulting inductance is higher than the inductance at high frequency when the skin effect becomes dominant. Wire Self Inductance Calculator Formula. Inductor calculator equation and structure for singlelayer coil type. If you are looking for braided wire, check out our full line of wire. e. To help you work most efficiently, we've created a number of calculating tools to aid in your wire and cable installations. Microstrip Inductance Calculator Trace Width (W) in mm: Substrate Height (h) in mm: Calculate Inductance FAQs. Keep units constant. This is the origin of the rule of thumb that the total inductance of a wire is about 25 nH/inch. 7 shows several types of inductors commonly used in circuits. These two signals make a complete loop. D = Coil diameter in centimetres. This tool calculates the inductance of a common object in electrical engineering: two parallel wires. The copper wires are parallel to each other, like. Total inductance of series-connected inductors is equal to the sum of the individual inductances. where M is defined to be the mutual inductance between the two devices. Trace Inductance Calculator. The wire’s radius is 0. Calculate the total mutual inductance that exists between the two coils. An inductor is typically made of a wire or other conductor wound into a coil, to increase the. number of turns. 11. The inductance of a solenoid can be stated as. In the model, the wire width of the coil is modelled as constant current-carrying filaments. Spiral Coil Inductance Calculator. Additionally, since the inductance is dependent upon its material surrounding, use Table-4 to determine an appropriate "K" factor (multiplier) for the inductance. Using our Solenoid Inductance calculator, you can easily find the inductance of a solenoid for different configurations. Tavakkoli et al. This rule of thumb helps us estimate the total inductance in the return path of a connector or package lead. with the vacuum permeability µ₀ = 1. Inductance is going to be around 3500 nh for 10 feet. LC Meter LC200A. Serway, John W. Multiply the number of turns and diameter of the coil. Designed for very high saturation currents from 32 A to 83 A at 100 °C, the six new types cover a range of inductance values from 3. Edge Coupled Trace Inductance Calculator. 98µH). 1: Some of the magnetic field lines produced by the current in coil 1 pass through coil 2. · My new Samsung plasma television (PN43E450) came with three ferrite cores (Todaisu HT2629S), a. Kim et al. Inductance is a property of electrical circuits that causes a voltage to be induced in a conductor when the current in the conductor changes. 37mm2, and a Rubadue S11NC133ECC-7 has an area of 4. Flat Wire Inductance Calculator. The wire’s radius is 0. Capacitance (C) = pF/ cm. Request PDF | On Jun 1, 2018, Cuili Chen and others published Junction Temperature Estimation for IGBT Modules Applied to EVs Based on High-Frequency Signal Sweeping Technique | Find, read and. Calculating limitations: The winding pitch cannot exceed the doubled wire diameter; Coil diameter cannot be greater than the doubled diameter of the rod ; Winding length should be less than 3/4 length of the rod; When the coil is shifting it should not reach the edge of the core 1/8 of its length; The initial magnetic. according to Rosa, 1,4,5 • A round wire mutual-inductance correction factor k. inductance of the loop can be expressed as the sum of the inductances of the two half-loops above the top plane and the inductance of the loop between the planes. Transformers only work with changing voltages. For number of coil turns: N= square root (L. If you don’t already have one, consider getting a breadboard. A round wire self-inductance correction factor k s according to Rosa, 1,4,5; A round wire mutual-inductance correction factor k m according to Knight, 1,6; A reduced effective coil diameter for modelling the current quenching in the wire under the proximity effect of nearby windings, The classic formula for single-layer inductance (air core) is called Wheeler's formula, which dates back to the radio days of the 1920s: where: L = inductance in micro-Henries (not nano-Henries!) N= number of turns of wire. . Input the values into the formula and calculate the self-inductance. The formula for calculating the Inductance of a cable is given by: L = K + 0. 25664 * 10-6 T*m/A. Equation $$L_{coil} = frac{ mu_{r} mu_{0} N^{2}. The inductance, L , per core of a 3-core cable or of three single-core cables comprises two parts namely the self-inductance of the conductor and the mutual inductance with other cores. 643 mm and wire’s centre is placed 5 mm over the ground plane. . The inductance of an air core coil inductor can be also calculated using the below equation. F. Enter the coil length (distance from first to last winding - see diagram). 60] has worked out a variety of cases for polygons with side length s and wire. Parameters . The most of the similar calculators work using Wheeler's formula, which has acceptable accuracy only when calculating the "optimal coil". length. There are some advantages to using a microstrip transmission line over other alternatives. 01 pF - 100mF. Publisher: Cengage Learning. Permeability (µ) is assumed to be 1. The magnetic field strength depends on the magnitude of the electric current, and follows any changes in the magnitude of the current. 081 uH. The new formulae show a substantial improvement in accuracy for short wires. Flat Wire Inductor For a flat wire, ribbon or PCB track, showing the formula used. Jewett. Value of inductance is normally directly proportional to diameter of the coil and a square of number of turns. Use this online calculator to determine the impedance, inductance, and propagation delay of parallel wires in an electrical circuit. 684e-12 F. Assumptions and Limitations Dimensions are in meters. Conductors are assumed to have zero thickness. Conductors is assumed to have zero. 75mm which equates to 23. The double integral of Neumann’s formula is computed numerically to evaluate the. Table 1 shows how to calculate inductance (L). Section . It is more difficult to calculate the mutual inductance of the rectangular coils with lateral or angular misalignment. Conductors are assumed to have zero thickness. DC resistances are as low as 0. 2 x d2x N2) / (3d + 9l =10b) L = Inductance (in μH) d = Diameter of the inductor coil (Inches) l = Length of the indutor coil (inches) b = Diameter of the coil winding wire (inches) N = Total turns of wire. Where: Lwop L w o p = inductance of the wire over plane in henries (H) μ0 μ 0 = permeability of free space = 4π×10−7. And you can input any four of the five components of the inductance formula to retrieve the fifth. 992e-2 Ohms. g. The inductance calculated using this tool is the external inductance of a rectangular loop of wire. Select the. Equation. 7 mm with insulation). Similarly, the leakage inductance can be a part of a reso-nant impedance that enables soft switching [3], [4]. Self-inductance refers to the inductance of a single conductor due to its own magnetic. Grover's Inductance Calculations - Working Formulas and Tables, is used. ured inductance of the wire). The classic formula for single-layer inductance (air core) is called Wheeler's formula, which dates back to the radio days of the 1920s: where: L = inductance in micro-Henries (not nano-Henries!) N= number of turns of wire. Lwire=2l⎧⎨⎩ln⎡⎣(2LD)⎛⎝1+√1+(D2L)2⎞⎠⎤⎦−√1+(D2L)2+μ4+(D2L)⎫⎬⎭Lwire=2l{ln[(…[μH] where L flat: inductance of the conductor [μH] ℓ : length of the conductor [mm] w: width of the conductor [mm] t: thickness of the conductor [mm]This tool is designed to calculate the inductance of a square loop of wire given its dimensions (width, height and diameter of the wire used). I might add that if you're looking to calculate the electrical impedance of a circuit, they have a separate impedance matching calculator and a PCB impedance calculator for various PCB-mounted conductors. Please provide a rating, it takes seconds and helps us to keep this resource free for all to use. Example: Find the impedance of a coil with a wire resistance of 2. Inverting Schmitt Trigger For an Op-Amp in an inverting configuration, showing the formulas used. For each case, we use a different cable impedance formula: To calculate the impedance of a coaxial cable, we use the following formula: Impedance = 60 × ln ( D 2 / D 1) ε r. The flux linked by the circuit is the flux found in the region between the two wires. Flat Wire Inductance Calculator. μr is the relative magnetic permeability of the core material. 0uH. The mutual inductance M21 of coil 2 with respect to coil 1 is the ratio of the flux through the N2 turns of coil 2 produced by the magnetic field of the current in coil 1, divided by that current, that is, M21 = N2Φ21 I1. r = Coil radius in inches. μr μ r = relative permeability. Choose a calculator to tune your PCB design. Graph Paper. As is known, such a structure is defined as the small inductances and capacitances distributed along the line length. Measurement accuracy:1%. 000uH to 100. m. Both round and flat variants of wire braid can be found under a few different call numbers, including AA59569 Mil-Spec braid which was formerly regulated b the QQ-B-575 military specification. Description The inductance calculated using this tool is the inductance of the loop bounded by the. Select the box with the geometry that you would like to calculate. Also, these calculators allow calculating just a ready-made coil. Here are the simple handbook formulas for the calculation of inductance, which Coil64 does not use, but which can be useful for electronics hobbyists and students. Coplanar traces where one trace is the signal and the other trace is the return path apply to this inductance calculator. Add the products of the coil diameter and 18 with wire length and 40 to get the denominator. Inductance Calculators. 6 Symbol used to represent an inductor in a circuit. Characteristic Impedance Calculator for the Measurement of PCB Tracks and Coaxial Cables Using a Vector Network Analyser. The calculator allows calculating the number of windings of the multilayer air core coil on a rectangular former at the design stage. It can only be solved indirectly, by calculating the inductance of many coils, subject to any constraints, and by choosing the design whose inductance matches the predefined value best, e. In electromagnetic compatibility (EMC). 2. 17mm2. Introduction of Coil Physical Properties Calculator. 00mF capacitance, 0. The inductance and inductive reactance of three single phase cables is provided by the formulas below. Find magnetic permeability and inductance factor of an unknown ferrite toroid core. No closed-form exists to calculate the inductance of a generic polygon of wire. 10. [1] The. (2) θ = 2 π N. Coil Inductance Calculator. Regarding current sheet inductance formulas for single-layer coils, one of the most widely known is the one by Wheeler [2], which states (after converting to metric units): L = (d 2 n 2) / (l + 0. The next point is very important. Having this in consideration, together with the particularities of planar coils previously mentioned, the complexity associated with the auto-inductance calculation for flat. It is assumed that this shield is sufficiently thick. 50 cm in diameter and 4. To reduction of overall dimensions of the coil and number of turns apply magnetic cores - ring, armored. 66. (2) θ = 2 π N. C. using an optimization method. X Length of Wire. Closely Wound Toroid. In Figure 3-3, one of the flat strips is re-placed by 4 wires. The transmission line geometries are cross sections and the. For a notionally thin wire, you can say that the magnetic flux produced by any part of the flow of current couples to flux produced by all other parts of the flow of current. $0. Use DigiKey’s Ohm’s Law calculator to calculate the relationships between current, voltage, resistance, and power in simple resistive circuits. Inductors, also know as choke, coil, or reactor is a passive electrical component that stores energy in its magnetic field. The capacitance is a function only of the geometry (including their distance) of the conductors and the permittivity of the dielectric. [μH] where L flat: inductance of the conductor [μH] ℓ : length of the conductor [mm] w: width of the conductor [mm] t: thickness of the conductor [mm] Inductance Calculator. Flat spiral air core coil inductor design calculator solving for inductance given wire coil number of turns, core material permeability, coil area and average coil length. d d = coaxial cable inner diameter. A flat spiral coil is a type of an air core inductor usually incorporated in the primary of a tesla generator, RFID tag, and proximity detectors. The calculator allows calculating the number of windings of the multilayer air core coil on a rectangular former at the design stage. The hidden assumption is that the wire is really part of a loop! For example, take an axial lead resistor, mounted to a. This calculator is designed to compute the inductance of a loop of wire given the diameter of the loop and the diameter of the wire used for the loop. Note that the input inductance should be in nano henries (10 -9 H). So, that is, 25 x OD x 2 times. W. It is far simpler to buy flat wire coils than to produce them. P. At VHF and UHF frequencies the inductance of a wire may have a great effect on a circuit. What is the mutual inductance? We need to know the radius, so assume its 1/2 * 0. The round-wire geometries are loops of wire with various shapes. Step 1: In the input field, enter the capacitance, inductance, and x for the unknown. 127mm times 92 raised. • A round wire self-inductance correction factor k. To calculate the inductance of a multi-turn circular wire loop, multiply the above formula by N 2, where N is the number of turns. Calculate the A. PI Network Impedance Matching. The inductance of a straight wire and coil with a given inductance in micro Henry the. Meter can measure 0. l is the length. Inductor Calculators. Our tools will help simplify the process. Ground plane is assumed to be perfectly conducting and of infinite extent. 10. (We are only concerned with the external inductance here. 1. Enter the length of the conductor: cm. 2. Calculator. The above expression is the inductance per phase of a 3-phase transmission line with unsymmetrical spacing but lines are transposed. Studying transmission lines I am confused about a "missing" factor of two in the formula L =μ0a/b L = μ 0 a / b for the inductance per unit length of two "infinite" parallel sheets. 75 instead 2. Coplanar traces are common in printed circuit boards. There are also formulae for single layer long coils, multi-layer short coils and flat "pancake" coils found at this page. I selected a 56-pF NPO capacitor for the tuned circuit because it is in the right range, and a dozen or so were in my junk box. For very high frequencies the inner inductance gets zero and the overall inductance tends to its outer inductance. (4-3), therefore, I needed a 2- H inductor. Divide the numerator with the denominator to obtain the inductance of the helical coil. The inductance for a rectangle loop is: where. If the windings are fixed in place, then this force is unable to do work (i. In the field of Physics, coil inductance refers to the property of a coil or an inductor to oppose changes in current flowing through it. C. according to Knight, 1,6 • A reduced effective coil diameter for modelling the current quenching in the wire under the proximity effect of nearby windings, • A series AC resistance for modelling the. One formula for inductance is as follows: Where: L = inductance. A coil inductance formula is based on the basic loop inductance. Dimensions are in meters. This keeps the inductance low, but also the bulk of the antenna thin / narrow. ϵr ϵ r = relative permittivity of the dielectric between the plane (s) and the wire. 5 mm 2. Phased-array radiofrequency (RF) coils are commonly used for signal reception in magnetic resonance for their large spatial coverage, typical of volume coils, and for their high signal-to-noise ratio, usually associated with surface coils. In this tool, the variables required are length and wire diameter. Wire Self Inductance Calculator. Always bear in mind that there is a tolerance on the stated AL value of a core. A precision laboratory resistor is made of a coil of wire 1. Note this is not the self-inductance of the wire but, rather, a closed loop. The online calculator uses the wire diameter to determine its length and the possibility of fitting it in the inner diameter of the toroid. density of steel. Trace Inductance calculator for wide traces over a ground plane with trace width (W) much larger than substrate thickness (T). r = average winding radius in inches. 99. Conductor is assumed to have zero thickness and to have uniform height. Within the wire, it increases linearly outwards from the centerline, and outside of the wire it falls off as 1/ r, where r is the radius. Scientific Calculator. L = (Dc × N)² / (18 × Dc + 40 × Lw). Flat Spiral Air Core Coil Inductor Design Equations Formulas Calculator. Having this in consideration, together with the particularities of planar coils previously mentioned, the complexity associated with the auto-inductance calculation. The HCV utilize flat-wire construction with low DCR and high efficiency performance. Use our free online coil inductance. With this approx-imation, the effective diameter D. ex. This optimal multilayer coil is called a Brooks coil. Can someone please help I need to find the coil inductance of 1650 turns 32 GA wire with 52. To calculate the capacitance in a parallel plate capacitor: Assume that the plates have identical sizes, and identify their area A. An insulated coil of N2 turns is wrapped around it, as shown in Figure 11. The calculation is based on the classic Wheeler's formula for single-layer inductance (air core, tightly wound), which dates back to the radio days of the 1920s: L = 0. Measuring Inductance Range: 0. ТThus, to calculate the inductance of a Tesla's flat spiral coil by the Maxwell's method. 00 cm long. Round Wire Inductance Calculator. 001N2D/ ( (228D/2) + 254l) Where: L is the inductance in henry's. 00H inductance and 0. Related Products: Magnetics, Transformer MiscSelect the box with the geometry that you would like to calculate. 2. Wheeler’s spiral formula is 1% accurate for c>0. Dimensions are in meters. ) coils, by setting the number of turns per layer, NT to 1 and setting the. To calculate the inductance of a single-layer, air-core coil: Select the measurement units (inches or centimeters). A long solenoid with length l and a cross-sectional area A consists of N1 turns of wire. Optimization results for example 2. 16 * X * ln (2*H/D) Where, X = Length of wire in in. In addition. Input (number of turns) N = (length of one side) W = (wire radius) a. Where: Lcoil L c o i l = inductance of the coil in henries (H) μr μ r = relative permeability of the core (dimensionless) μ0 μ 0 = permeability of free space = 4π × 10−7 4 π × 10 − 7 (H/m) N N = number of turns. Dimensional units: mm mils d1 (outer diameter) = d2 (inner diameter) = N (number of turns) = L (Inductance, nH) =. Mean Length of Wire Turn (MLT) on the particular core 3. Li is inductance distrib-uted within the wire, from the surface to the center . Wire gauge calculations Wire diameter calculations. The inductor impedance calculator calculates the impedance of an inductor based on the value of the inductance, L, of the inductor and the frequency, f, of the signal passing through the inductor, according to the formula, XL= 2πfL. Propagation Delay (T pd) = ps/ cm. kL: field non-uniformity correction factor according to Lundin. Square the resultant to obtain the numerator. Assumptions and Limitations Dimensions are in meters. Yours calculated 3. F. If, on the other hand, a < δs or merely ∼ δs, then current density is significant throughout the wire, including along the axis of the wire. Touch the red wire to the exposed end of the resistor and the black wire to the opposite end of the inductor. Ground plane is assumed to be perfectly conducting and of infinite extent. PCB Structures / Discrete Structures / Signal Management. Rectangle Inductance Description. The inputs. Lcoil = μrμ0N 2A l = μrμ0N 2πr2 l L c o i l = μ r μ 0 N 2 A l = μ r μ 0 N 2 π r 2 l. Here it is in terms of D, the diameter of the coil:The inductance, L, is defined in terms of the current, I, flowing through the system, and Wm, the magnetic energy density is proportional to B2. This algorithm is applied in Coil64, online calculator, as well as in versions Coil32 for Android and Linux, to increase the accuracy of the calculation of the inductance of single-layer air core inductor. N: number of turns. All of the above logic of reasoning and derivation of formulas, starting from the Neumann formula. 14 AWG instead of 16 AWG) or 1. For more information see About our calculators See full list on allaboutcircuits. Single Dual Triple Quadruple. The inductance of the coplanar trace calculation requires 4 variables: W - Trace Width; S - Trace Seperation; L - Trace LengthMutual inductance is where the magnetic field generated by a coil of wire induces voltage in an adjacent coil of wire. Having this in consideration, together with the particularities of planar coils previously mentioned, the complexity associated with the auto-inductance calculation. 62) 19. Itisatonceevidentthatinthelimitingcaseofanextremely. The mutual partial inductance is calculated as mutual inductance be-tween two filaments and provides exact values [1]. Dimensions are in meters. L = µΓéÇ * N² * A/l. Corrected Inductance is the Current Sheet Inductance value with corrections for round wire and frequency included. This calculator allows calculating the number of windings of the multilayer coil at the design stage. loop area and wire radius. 00pF to 100. ferrite "rings" or "collars". While this is a “round wire” formula, it may still be applicable to. d = Winding depth in inches. b. This image from AllAboutCircuits, shows various coil cross sections, and their corresponding (approximate) inductance formulae. Coplanar Capacitance. g. To. Ohm’s Law Calculator. Dimensional units:. A microstrip is a flat conductor separated by insulating dielectric from a large conducting ground plane. Wind the wire as cleanly and closely as possible, and apply CA glue during the process to secure. The equation above is from “Inductance Calculations” by F. Alternatively, you. Where: L is the inductance of the air core coil in henries (H) μ 0 is the permeability of free space (4π × 10 -7 H/m) μ r is the relative permeability of the core material (dimensionless) N is the number of turns in the coil. Advanced Crystal Radio Initiative Calculator £ 6. Internal inductance is not included in this model, but may be calculated using the Wire Internal Inductance tool. The inductance in the form of a round loop is calculated by the formula: where: L - inductance [H];; D - diameter of the loop [m];; d - diameter of the wire [m];; μ 0 = 4π·10-7 permeability of free space;; μ - relative magnetic permeability of the conductor;; You can often find the last formula in which the last member of the equation is 1.