The differential pair—sometimes called the long-tailed pair—is a widely used building block in electronic circuits, particularly in op amps. Stack Symmetry – enable to add layers in matching pairs, centered around the mid-dielectric layer. When you are creating your schematic, you must use one of the following suffixes when naming your differential pair nets: +/- (e. PCB Structures / Discrete Structures / Signal Management. Actually the "odd impedance" is the correct impedance to look at for the USB requirement of 90 Ohms differential impedance. Its utility stems from its ability to. Altium Designer’s rules-driven design engine allows you to define trace length tolerances in differential pairs and across signal nets. Differential pairs should be tightly coupled throughout their entire length, so try to avoid variations due to pads, vias, or components along the routing path. 03) it gives me almost 160 Ohm - and even if use 53mil conductor height or. Route differential pairs symmetrically and keep signals always parallel. 30967mm) is slightly larger the size of the smallest pad (0. When you are creating your schematic, you must use one of the following suffixes when naming your differential pair nets: +/- (e. Differential Pairs 101. too. Reference: R. Once the option is active, click on the shortest trace and move the mouse. Use via-s (absolutely not recommended for impedance-critical routes) hack the connector and remove some of its SMD pins, and wire one pair under those pins. An input voltage between the two gate terminals produces an output current in the drain terminals. 9. The following options in the Options for PCB Project dialog are used to configure this:. If you do something else with the. This simple impedance calculator had a number of limitations, including requiring return paths to be implemented by plane layers, only supporting symmetrical stripline board structures, and no support for differential impedance calculations. when i use Saturn PCB design to match the differential impedance to 100ohms i get 0. Differential pairs: even or common mode?PCB impedance calculator – Single ended / Differential pair. Unfortunately Online Calculators are deceiving unless you actually draw the numbers and understand the ratios and tolerance effects. Ask the board manufacturer for the values. Figure 81 shows the topology. The Si8000 Quick Solver is convenient to use for this purpose, as shown in Figure 4. balanced), above a ground plane, have an impedance. Before we can start routing the PCB, we need to define Design Rules for our differential traces. Differential pair routing. 3mm, as shown below: This increases the impedance slightly to 91. 1<W/H<3. This kind of functionality is present in only some PCB design programs, and those with it have varying degrees of accuracy in their output. Joined Jan 22, 2008 Messages 51,800 Helped 14,703 Reputation 29,682 Reaction score 13,944 Trophy points 1,393 LocationWhile there are a number of online calculators that calculate the characteristic impedance from the input geometry, they are all based on approximations. distance between the differential stripline pair: er: relative permittivity of the dielectric: Electrical Parameter Definitions: Zo:In PCB design software with a built-in impedance calculator function, you can calculate impedance quickly. 35,851. FWIW, the calculator I've used in the past is called Polar SI8000 which apparently has been superceded by Speedstack PCB. These values are trace width, substrate heights, substrate dielectric, and trace thickness. Such a stripline is constructed with two traces referenced to the same reference planes above and below the traces with a dielectric material between them. The Differential Pair Impedance Calculator is a specialized tool used in electrical engineering and signal integrity analysis to determine the characteristic impedance of a differential pair of transmission lines. This rule maintains the desired signal impedance. There are single end trace impedance and distance between traces in the pair. D+ and D-) _P/_N (e. Most often, the only specified requirement of a differential pair is its differential impedance. The odd mode impedance is the impedance of one transmission line when the pair is driven differentially. 6 inches - this is very easy to do; If you can access a differential impedance calculator, then use differential. As you can see, calculating the twisted pair characteristic impedance by hand using Eq. Compatible with Flex PCBs and Turnkey PRO service. Try to keep all other high-speed traces at least 0. There is only one method I am aware of that gives any level of accuracy for differential via impedance calculations, and it starts from a calculation of the propagation delay through a pair of differential vias. Edge Coupled Stripline Impedance Overview. The single 50 Ohms is the impedance of a single-ended transmission line that has a ground connection. Calculate Z 0 as normal Microstrip, until you get the desired value, e. Enter the relative permitivity, width of the trace, the ground plane spacing, and the substrate thickness to calculate the characteristic impedance. There are various ways to de-skew a differential pair: in the via anti-pad area or in the trace. The JLCPCB Impedance Calculator computes track width values and recommended stack-ups from user-input values of board layer, thickness, copper weight, target impedance, trace spacing (for edge-coupled pairs), and impedance trace to copper gap (coplanar waveguides). Unfortunately, TxLine doesn't do coplanar waveguide for differential traces. The designer needs to create a stackup for the board and then calculate the trace values for differential pairs and single-ended nets. It incorporates many features that PCB designers and engineers are in regular need of like current capacity of a PCB trace, via current, differential pairs and much more. Just enter the given values for trace thickness. If we want to hit the standard 50 Ohms impedance target, then we need to have a trace width of almost 110 mils!Differential microstrip and stripline pairs have common-mode noise immunity if they are routed symmetrically, but they also need to have controlled differential impedance to ensure impedance matching and consistent propagation delay throughout an interconnect. This sets the single-ended impedance AND differential impedance to the target value, even if there is no. Other calculators will use different. Thus, for optimal performance the resistors and MOSFETs must be matched. USB 2 e. And since no return current flows through ground (or so it is assumed) then the terminating resisters are connected in series between Traces 1 and 2, and the correct terminating impedance is calculated as 2(Zo – Z12). A differential amplifier multiplies the voltage difference between two inputs (Vin+ - Vin-) by some constant factor Ad, the differential gain. I tried using different line width (10mils,15mils,20mils,25mils,30mils) of the differential pair but it doesn’t help me. 25. Single Ended Impedance Ω. Placing a Differential Pair directive on each pair net applies a parameter to the net,. Jan 31, 2016 #2 FvM Super Moderator. To examine impedance variations, select the Impedance Workflow option in the analysis toolbar. Adjust the distance "s". Let's match the impedance of the same signal since differential pair routing is completed when the impedance is matched properly. 5 mil (2116 prepreg) or 8. It renders fairly accurate results suitable for use in circuit board manufacturing and engineering analysis. Use the Series and Shunt Impedance Calculator: to try your own impedances; Change Grid: S11, (ZL normalized to source impedance Z0) Z_Load: Z_Load: Matching Network Calculator. (Differential Impedance, Ohms) = Note: 1oz = 1. I am trying to design a USB circuit, where the signaling is over a differential pair D+ and D- and these two lines are required by the spec to have 90 ohms of differential impedance. Select the Calculator button. where Z 0,surf can be computed as specified in Eq. The allegro calculator gives a value of 56. Figure 4. Note: Units do not matter for this calculation as long as they are consistent. 68 mils. g. According to this guidelines, the differential pair (DP and DM signals of the USB) must have 90 ohm impedance to each other. The PCB design tools in Allegro include an impedance calculator that will help you size your traces so that they have defined characteristic impedance. 3 V, etc. The other yellow rectangle is the USB connector. The formula used in this calculator is an approximation for the characteristic impedance of a coplanar waveguide: scssCopy code. With the differential microstrip impedance calculator in Altium Designer,. to NFThe impedance of the structure is the ratio of the voltage between, and the current in, the conductors. It is often said that differential pairs do not have a return path, which is not true. Figure 4 illustrates the impedance of a differential STP and its connectors. Polar or rectangular grids only allow direct reading of S11. For an embedded (internal) microstrip, the formulas provided in paragraph 4. This is typically used when golfers play only a partial round or when a full 18-hole round isn’t completed. Choose a calculator to tune your PCB design. ”7. 5. 1-11. The amplitude increases as the coupling length increases up to a point. Sorted by: 1. Formula: Applicability: w ÷ t ≤ 0. 2. Figure 2. The values you get from an online differential pair impedance calculator corresponds to an isolated differential pair, they do not consider the load component and they are not calculating the input impedance. This means that the channel dimensions of both FETs must be the same and that R 1 must equal R 2. This calculator finds both odd and even transmission line impedance. In the image below, I am comparing differential vias with merged. EEWeb offers a free online broadside coupled stripline impedance calculator. The trace width (0. Differential impedance is twice the odd mode impedance. The resultant current is called common-mode current. 25mm between the differential pair with a width of 0. I use the software a lot to calculate impedance, maximum current for t. net Forum comes closest to the proper track width. 8. The twisted pair helps create a more. transmitted across a twisted pair cable by a differential line driver and sensed at the far end by a. The characteristic impedance is given by: Eq. There are four different types of impedance used in characterizing differential trace impedances. The following are typical line widths and spacings for the more common impedance values when using ½ OZ copper: 50 Ohm Single Ended: 0. Unfortunately Online Calculators are deceiving unless you actually draw the numbers and understand the ratios and tolerance effects. Ask the board manufacturer for the values. 19mm) traces with 7. Converts short and long line . TransCalc is an open-source impedance calculator of various transmission lines based on common closed-form approximations. 2 High-Speed Signal Trace Lengths As with all high-speed signals, keep total trace length for signal pairs to a minimum. Note that the y-axis is on a logarithmic scale for clarity. A microstrip line is a type of electrical transmission line used to convey microwave-frequency signals and consists of a conducting strip separated from a ground plane by a dielectric layer known as the. The source for formulas used in this calculator (except where otherwise noted) is the Design Guide for Electronic Packaging Utilizing High-Speed Techniques (4th Working Draft, IPC-2251, February 2001. The topology pre-dates the solid-state era and is generally attributed to Alan Blumlein, when it appeared in one of his patents in 1936. The interactive routing and differential pair length matching features in Altium Designer® can be used alongside an integrated electromagnetic solver in the Layer Stack Manager. Some differential impedance requirement for differential pairs, where the signals must be routed together Just as an example, consider a 2-layer board on standard thickness 62 mil core (Dk = 4. 1. In some cases, we can also use 75-ohm differential impedance. 4 Comments. To use this calculator, simply input your microstrip geometry and Dk value, and the tool will return the differential impedance value for a pair of microstrip traces. Speedstack Si – Insertion loss & impedance PCB stackup design including Si9000e. Disc Air Capacitor Calculator; Impedance Calculator : XL, XC; Inductors, Transformers. Yes, that's right. So, I am trying to figure out how to use Kicad’s PCB Calculator for “Coupled Microstrip Lines”: I’m unsure about what a couple of the parameters mean and can’t find an explanation in the docs (it just. Calculating the impedance . Altium Designer makes it easy to calculate geometry when you need to calculate impedance for differential pairs. This value is often given the name “differential impedance. For example, a single 0. 100 ohm differential pairs that are tightly coupled have a typical single ended impedance of around 65 ohms. Instant online PCB quote, get PCBs for only $2. The grounded differential coplanar wave guide is the differential version of the grounded coplanar wave guide and is used in high-speed digital systems that require maximum noise immunity. INPUT DATA. 2In real high speed signal pairs (like USB3) the pins are swappable to avoid the need to cross the traces. look at driving a twisted pair differentially from the FDA. In the special situation for which there is no coupling to ground, Differential impedance equals the Characteristic. Critical Signals (continued) Signal Name Description HDMI_DATA1x High-Definition Multimedia Interface (HDMI) differential data pair, positive or negativeFor example, the equation for the trace impedance in a differential pair of asymmetric striplines includes an approximation on the dielectric constant and geometry. Near 50 ohms, many of these approximations are within a few percent accurate. These calculators will return an impedance value for pairs of trace width, substrate thickness, and copper weight values. Edge-Coupled Microstrip. Differential pairs with vias and right-angle bends are acceptable. To find the impedance of a capacitor (Zc) and an inductor (Zl) in an AC circuit, you use the following formulas: For the capacitor: Zc = 1 / (2πfC) For the inductor: Zl = 2πfL Where f is the frequency, C is the capacitance, and L is the inductance. This sheet has the FTDI chip which converts the input serial signal into a USB differential signal. High-speed differential pair signal traces need to be routed parallel to each other with a constant spacing between them. This means the slope resistance is 7 V 0. PCB manufacturer normally provides information about PCB stackup and track geometry. There are some signal integrity issues with de-skewing in traces: Impedance. We get a lot of questions about trace impedance and how to calculate the right trace size to hit a specific impedance in a manufacturable PCB. • If finite tail impedance and asymmetry are both. e. The closer you place the pairs together, the differential impedance gets smaller because LM and CM get larger. While the edge couple differential symmetric stripline transmission line is a common technique for routing differential traces. This is the impedance between the two signal traces of a pair. A twisted-pair cable is simply two wires that are twisted together so as to reduce radiated EMI (electromagneticinterference) and mitigate the effects of received EMI. 5 mil wide traces with about 6 mils of gap between the traces. 5 mil (2116 prepreg) or 8. How field solvers such as the Si8000/9000 calculate impedance. Fig 1. Even mode impedance for commonly-driven transmission lines . 62 Ohms. This slope resistance, in parallel with the collector resistor (Rc) dictates what the output resistance of the amplifier is. High-quality circuit boards as prototype and series at reasonable prices. This video will cover how to create, setup rules, and route differential pairs. Dimensional units: mm mils. 2. is the impedance between two differential pair signal traces. Incidentally, analog signal integrity may be a bigger problem than digital in this design. Both LM and CM converge to zero as spacing goes to infinity. Similarly, external fields can induce currents in a differential pair that are not equal in amplitude and opposite in phase. 0. Zdiff is the impedance between the two traces of a differential pair which equals 2 x Zodd Zcom is the impedance between the two traces of a common mode pair which equals Zeven / 2 Edit: You may have noticed that the mantaro calculators give a slightly different result of 12 mil and 12 mil. In general, it works and can establish a Link with 1 Gig, but when exchanging multiple Gigabyte of Data it starts to cut out and collect RX Errors. on layer 3 from the top, between power and ground plane. You want to select “Microstrip Zdiff”. Differential Stripline Impedance Calculator. Details: In the list below, [1] is the reference design stackup information; [2] and [3] are the processes to get the result close enough to the reference design target so as to know the tool is valid; and [4] is the calculation in question because it is either 5. > There are a lot of impedance calculators on the web but none seem to match each other. A printed circuit board (PCB) mechanically supports and electrically connects electronic components on a circuit board. The differential pair impedance depends on the characteristic impedance and the spacing between each end of the differential pair. So, to calculate the differential impedance of Figure 1, simply calculate the impedance of Figure 3, and double it. PCB Impedance and Capacitance Calculator: Asymmetric Stripline. We’ll go over how differential pairs can hel. 25, but gives me nice trace from the module to the stub then to microcontroller. Learn how to design. Differential pairs are commonly found in high-speed data communication systems, such as those used in computer interfaces (e. Calculates the differential pair impedance of a balanced line. e. Then Right click -> Create-> Differential pair. 29 mm width traces to obtain 100 Ohms ZDiff while using 0. Download the file here. Hello! I'm trying to calculate the trace width for a differential pair (carrying MIPI CSI-2 signals), using JLC's impedance calculator. i know that i can use. So, I am trying to figure out how to use Kicad’s PCB Calculator for “Coupled Microstrip Lines”: I’m unsure about what a couple of the parameters mean and can’t find. No, the single-ended impedance provided in differential line calculators does not matter. Don’t ignore ESD. This resistor is invisible to the even mode signals as the even mode content on each track is identical so no even mode current flows in this resistor. Try TNT or TxLine. The microstrip is a very simple yet useful way to create a transmission line with a PCB. Free!!! $5 Registration Link: link : on Setup -> Constraints > Electrical Constraints Set - > Differential Pair Value - > Calculator > If you put 10 in the Line Width, the calculator calculates the single ended as well as differential impedance. Using a differential pair to avoid common mode noise is common in audio circuits. Microstrip construction consists of a differential pair and a single reference layer (typically ground). Another example of using large distances to separate out unwanted components might be to calculate the impedance of a. 6. High speed PCBs and signaling standards almost entirely use differential pairs with precise impedance. This calculator is designed to calculate the characteristic impedance of a microstrip - a flat conductor suspended over a ground plane with a dielectric between them (see diagram below). A cheap unshielded laminated polyester FPC cable with 0. best to use a stackup calculator to provide quick ‘what if’ analysis of the possibilities. 2. Ready to give CircuitStudio a try? Click here to get started: impedance. Return loss is an important parameter that indicates how well the impedance matches with aFor differential vias, stitching vias can affect the impedance, but the impedance is much more sensitive to antipad sizes and layer arrangement/Dk value on each layer. Using the formula, you can calculate the Differential Impedance (Zd) as follows: Zd = 2 * 100 / sqrt (1 + (2 * 100 / 20)) Zd = 200 / sqrt (1 + 10) Zd = 200 / sqrt (11) Zd ≈ 60. It is designed for precision signal. mils: Distance between planes (B) mils: Relative Dielectric constant (Er) Differential Trace Impedance: ohms: References. To calculate the values, the designer needs to know the following information: Number of board layers• As shown in Figure 1, traces should be 100-Ω(±5%) differential impedance of differential microstrip or differential stripline. The differential pair—sometimes called the long-tailed pair—is a widely used building block in electronic circuits, particularly in op amps. Most online calculators do not account for copper roughness. 1. Differential pairs should be tightly coupled throughout their entire length, so try to avoid variations due to pads, vias, or components along the routing path. Joined Jan 22, 2008 Messages 51,800 Helped 14,703 Reputation 29,682 Reaction score 13,944 Trophy points 1,393 LocationDifferential Pair Calculator The Differential Pair Calculator is used to perform what-if analysis to determine what values of Primary gap and width are needed to get specific differential and single line impedance. Differential pairs are very simple: they are composed of two traces, routed side-by-side, and that carry equal magnitude and opposite polarity signals on each trace. A cross-hatch plane is shown in the image below. The impedance of a differential via pair cannot be treated with a single via impedance calculator unless the vias are spaced far apart. has two length-matched 45 Ohm lines. Enter the number n n of impedances in parallel as a whole number and press "Enter". 331 1 2 5. Coplanar Waveguide Calculator. As you route your board, the built-in trace length calculator will check your routing against your design rules and flag errors for correction. e. Go to Route > click tune differential pair skew/phase > click on any of the track. You can define Min Line Spacing, Primary Gap, Primary Width, Neck Gap, Neck Width, + and – Tolerance as either a Physical or Electrical CSet. To use this calculator, simply input your microstrip geometry and Dk value, and the tool will return the differential impedance value for a pair of microstrip traces. This release sees the introduction of the Simbeor® electromagnetic Signal Integrity engine. Now select the two nets that you want to declare differential. Differential pair on a reference plane for differential mode (left picture) and common mode (right picture) line impedance In addition to the four line impedance types the Impedance Calculator is also able to calculate the Coupling Factor between two traces on either the same signal layer (horizontal coupling) or between two traces on different. CAN bus layout design. Build a model from experimental data of impedance vs. Activity points. Please provide a rating, it takes seconds and helps us to keep this resource free for all to use. button. The calculation looks correct, but the tracks are too wide. They will give very similar answers. Differential and Common-Mode Impedance 2. A golf handicap calculation based on the score achieved for nine holes of golf. Let us now calculate the differential impedance. The concept of Shield Transfer Impedance (Zt), introduced by S. The calculator shows 90 ohms can be achieved using. The test sample consists of a pair of differential traces at the top layer, followed by a differential via to the inner traces, then a second differential via connects to the BGA landing pads at the top layer again. The transistor pair is matched for minimum offset voltage and differential thermal response. Inductance (L) = nH/ cm. I also have power connector to carry power one side to other. Cross-hatched copper plane in a flex stack-up for controlled impedance. Most of the dedicated TL tools doesn't have this option, only if you use a full EM simulator. 0 and 0. $egingroup$ @Bryce, whether the individual line's impedance is half the differential impedance depends on whether the pair is "strongly coupled" or "weakly coupled". g. Length matching is required per segment, and any length added (typically a ‘serpentine’ section) for the sake of matching a pair should be added near the location where the mismatch occurs. You will need to know the dielectric constant and the copper thickness to calculate trace impedance. Fig 2b Equivalent. , D+ and D- (TSKEW)) must be less than 100 ps and is measured as described in. Differential Stripline Impedance Calculator. Zeven: This is the even-mode impedance of the differential pair. Also, it has got. Twisted pair: \qquad \footnotesize \text {Impedance} = \frac {120 \times \ln (2s/d)} {\sqrt {\varepsilon_r}} Impedance = εr120 × ln(2s/d) As you can see, it is not overly complicated to calculate by hand, but it will definitely take longer than using our calculator. Comparator tab . , equal in magnitude but opposite in polarity). . 1. This 100 Ohm has no ground connection. You can calculate it with the following equation: Z (z) = V (z)/I (z). Testing and modelling characteristic impedance of differential pairs without ground. D_P and D_N) KiCad looks for these suffix pairs when using the differential pair routing tool during PCB layout. Eurocircuits’ Impedance calculator uses real values as defined in the supplier’s data sheets. PCB impedance calculator – Single ended / Differential pair PCB manufacturer normally provides information about PCB stackup and track geometry. In a previous article, we have seen how to route a differential pair signal. 08mm - this is the border of manufacturability, I don't think it is practical to go there but for the calculation it is just fun - and I get some 31Ohms. Even and Odd Mode Impedance 3. A PCB impedance calculator is necessary to set the constraints for trace structures during fabrication; they can vary in complexity, speed, and accuracy. look at a differential source driving a twisted pair to the FDA. A differential pair consists of two well matched, source-coupled transistors as shown in Figure 6-1. In addition to the characteristic impedance of a transmission line, the tool also calculates: This calculator is designed to calculate the characteristic impedance of an edge coupled stripline. Phone: +44 (0)1425 489 111 / +49 (0) 8104 628 0. This calculator is designed to calculate the characteristic impedance of a broadside couple stripline (see diagram below). But, you usually want some decent coupling between the traces, so a good single-ended impedance target for each trace is between. Two conductors can create a transmission line. The rules shown below are a rough approximation, and you should always check the approximation using an impedance calculator or field solver. By Perrine Juillion / April 8, 2020. Our impedance calculator features two main types of impedance models, single-ended and differential, within each trace structure. Coaxial Line Impedance. For double termination, we want the source to provide R S = 50 W on each side for 100-W differential output impedance, and we want the input of the FDA to present a 100-W dif-ferential load. Twisted Pair Impedance Calculator . 25, but gives me nice trace from the module to the stub then to microcontroller. Adding stitching vias adds distributed capacitance in. Edge coupled differential pair Edge coupled internal symmetric differential pair Edge coupled internal. g. 004” line/0. This ensures that the receiver. Note that the net pair must be named with net label suffixes of _N and _P. In Altium Designer you can easily change the width of both of the differential pair tracks, but if you do so the gap of the diff pair changes depending on the change of the width. GEGCalculators. The procedure for calculating the differential impedance of an interconnect with a differential via transition is iterative; you calculate the input impedance from the. This makes the problem of determining impedance much more complex, and building an initial lossless model requires a larger set of formulas. The two traces of a pair should be symmetrically routed. 2Distance units: Substrate Height, H Trace Width, W Thickness, TFigure 1. To achieve this, I used the built-in Calculator in KiCad. case of Figure 1, the mismatch occurs between the characteristic impedance of the twisted pair (typically 100Ω) and the 4 kΩinput resistance of the DS26LS32A. Single-ended impedance of 50 Ohm. How to Use the Calculator. 8. To use these to design for a target impedance, simply cycle through various geometric values for the trace width until the calculator returns the target. These calculators give us essential trace spacing and differential pair spacing if needed. 5 and I took 3. Its utility stems from its ability to. 3. 225m s = 2mm. These values are trace width, substrate heights, substrate dielectric, and trace thickness. This is a calculator used for determining the characteristic impedance of a microstrip. It uses the lan9512 reference schematic. But I'm unsure if the Height I entered is. Grounded Differential Coplanar Wave Guide. For double termination, the source needs to provide R O = 50 Ω on each side for a 100-Ω differential output imped-ance, and the line needs to be terminated with R L = 100 Ω. Simons, "Coplanar Waveguide Circuits, Components, and Systems", Wiley. Notes: 1) Calculation assumes traces are centered vertically. RS485 uses differential signaling for the cable of 100Ω or 120Ω, the terminating resistance should match the cable. Differential impedance, Z diff, is the impedance between the two conductors. microstrip Zo vs Edge Cpld Ext Zo). We care about maintaining the same differential impedance for. Note: The 6-Layer board temporarily only provides JLC3313 Stackup. The controlled impedance method applies to any trace that handles high-speed or high-frequency signals. However, it will definitely take longer compared to using a calculator. Coupling can, however, be used to advantage in the form of differential impedance. ’ Go to the ‘Differential pair rules’ >> ‘New rule. 1 has six signal layers, but only has one pair of planes closely spaced. I am trying to design a CAN bus node. Enter your board parameters and get instant results. This 8W rule also applies to ground planes on the same layer. 2 of the Microstrip Calculator, h=H1 and b=H2-H1. This means that the channel dimensions of both FETs must be the same and that R 1 must equal R 2. EEWeb offers a free online twisted pair impedance (transmission line) calculator. . .