Last Modified: July 22, 2014
Contents: Basics; Over Voltage Issues; Measuring Capacity; Alternator Ratings; Alternator Whine; Auxiliary Batteries; Mixing Battery Types; Battery Isolators; Battery Imbalance; Battery Boosters;
You almost can't have too large of an alternator!
All modern passenger vehicles come factory equipped with alternators. Peak amperage ratings range from 100 to as high as 275 amps. These high outputs ratings weren't meant for us amateurs. Instead, they're intended to provide the necessary power to defrost our windows, power navi systems, heat our seats and mirrors, and all the rest of the accessories we've become accustomed to. In addition, more and more vehicles are being equipped with electrically-driven water pumps, power steering motors, and even power brake assist.
With the advent of Fed-mandated Engine Idle Shutoff (EIS), they're bound to get even larger in terms of output power. EIS also requires more robust batteries, starter motors, and a means of assuring the SLI (Starting, Lights, Ignition) battery has enough reserve capacity (SOC—State Of Charge) to restart the engine when required. Depending on the make and model, Electrical Load Detectors (ELD), Battery Monitoring Systems (BMS), and Voltage Quality Modules (VQM) are often employed. These systems are also interconnected to the engine control computer.
The ELDs use a Hall device to measure the amperage load are typically located around the negative battery lead as shown in the left photo. Along with the load, the BMS's battery voltage measurement, and the ambient and engine temperatures, the engine control computer determines whether the engine should be shut down after a specific length of idle time. When it is shut down, VQMs are used to maintain the supply voltages to the various on-board accessories (radios, lights, etc.). Replacing the battery may require resetting the engine control computer (2002> BMW vehicles for example).
It is important to know what an alternator really is. In simple terms, automotive alternators consist of a rotating, claw-pole field which is nothing more than a rotating electromagnet. Both the north and south poles of the field are energized by a single winding. This rotating magnet (rotor) spins inside an inter-woven tri-filer wound stator coil producing a three phase AC output. This output is full-wave rectified producing a near ripple-free flow of current. By adjusting the amount of field current, the output can be maintained (regulated) at a constant level, nominally 14 VDC (13.6 to 14.4), up to the rated amperage of the unit.
In a load matched condition, the output power of a claw-pole alternator is proportional to the number of field ampere turns squared. With this in mind, both OEM and aftermarket rebuilders have started to use two, independent tri-filer wound stator coils, and 12 diodes instead of just 6. This nearly doubles the field ampere turns, which allows the alternator to be smaller, lighter and more powerful. The use of Schottky diodes with their low forward voltage drop adds further benefit. Multiple tri-filer windings also produce more output at lower engine RPMs. A few high-end suppliers offer alternators with three, tri-filer windings, and an 18 diode array! An example is shown above right as supplied by Alternator Parts. These units are capable of producing as much as 500 amps! About the only way to produce more, is to use multiple alternators which greatly exacerbates the wiring and regulation problems. Alternator Parts also offers their exclusive Quicktifier®. It is an external, fan-cooled diode pack which increases reliability, and reduces diode-switching RFI.
If your power needs are really big, you'd be better off with an on-board AC generator. Better yet, an Auragen system as shown at right. The AuraGen® is a new class of axially symmetric induction machines. The machine's design is really quite intriguing. It generates 400 volts AC, which is fed to an inverter, which supplies both battery charging current (nominal 14 vdc), as well as 120/240/480 volt AC—up to a total of 13 KW! The inverter can also operate backwards, supplying 120/240 voltage from a battery bank. Even if you don't own a huge motor home, the data on Auragen's web site is a good read.
The methodology used to regulate the output voltage varies with manufacturers. Some alternator regulators pulse the rotor current similar to a switching power supply, while the others (usually older models) use an analog method like a linear power supply. Similar to a switched bench supply, the frequency and/or the pulse width may be varied (independently or together). The RFI from these models sounds like the old cartoon rat-a-tat-tat used for machine gun sounds. Although it may sweep across the bandpass, that is not always the case. If you're plagued with this particular noise, the alternator's regulator is a good place to start looking.
It is by any measurement getting more complicated to install amateur radio gear (especially amplifiers) in a modern vehicle without circumventing or bypassing ELD, BMS, and VQM devices. However, if done properly even a second battery can be installed without causing any undue concerns. The first place to start is the Wiring article. If you're still in doubt, and especially so if your vehicle is equipped with any of the aforementioned devices, consult your dealership's service department for guidance.
The diodes used in most late-model vehicle alternators are more than just simple silicon diodes. They're typically Schottky types, and designed to break down and act like a reverse-biased zener diode should the output voltage exceed ≈18 volts. Thus they provide one level of load-dump transient (LDT) protection for on-board electronics should a battery connection be lost. If you properly maintain your electrical system, you shouldn't need them, but it is nice to know they're there in case you do!
It should pointed out, that some alternators have more diodes than mentioned above. For example, older model Ford alternators are Y (rather than delta) configured, and use 8 diodes.
Over Voltage Issues
A number of vehicles—primarily those with batteries located other than in the engine compartment—are equipped with alternator voltage regulators which are factory set (nominally) to 15.1 volts. Part of the strategy for such systems is LRC (Load Response Control). There is a whole lot more here than meets the eye, but the bottom line is to maintain the SOC (State Of Charge) of the battery. This is especially important in those vehicles which are equipped with EIS (Engine Idle Shutoff). These higher-than-normal voltage levels are designed to compensate for the voltage drop in the wiring from the alternator, and the battery (remember, the battery may be located in the trunk or within the interior of the vehicle). While this issue may appear not be of concern, it can be!
Alternator voltage regulators are designed to adjust their output voltage depending on the SOC, ambient temperature, the load impressed upon them, and even the age of the battery (see Advisory Comment below). Therefore, it is not uncommon for the output voltage to increase to ≈16 volts! This level is very close, if not exceeding, the rated limit of most modern-age transceivers!
As a battery ages, its ability to hold a charge, and the maximum state of that charge, diminishes. To compensate, the output voltage of the alternator is increased slightly. The algorithms used in modern Battery Monitoring Systems (BMS) have provisions for measuring the age-related decrease in battery capacity. The basic scenario is to occasionally deactivate the alternator, then measure the voltage drop over a short period of time under whatever load is present. The technical term for this methodology is Coulomb Counting. The sophistication of these systems are often good enough, that they can tell you when the battery needs replacing before any outward signs appear.
On the forefront of BMS technology are devices which measure the magnetic properties of the battery. Called quantum magnetism, the technique can not only measure the SOC, it can also measure the reserve capacity even during charging and discharging. The technique is far more accurate than Coulomb Counting, but currently is too expensive to put into general use.
Cadex, a Canadian company, has developed yet another battery monitoring methodology called electrochemical impedance spectroscopy. It is capable of measuring CCA to ±5%, and SOC to ±20%. However, EIS as it is known, is an expensive and complicated technology. Developing it to meet OEM standards and cost restraints, will take time.
In the old days, most all cars were equipped with ammeters connected between the battery and generator. It was easy to see if the generator was delivering enough current. With the advent of alternators, the ammeter lost its effectiveness. The reason is, electronically controlled alternators always put out just the right amount of current. So, except for brief periods, an ammeter would always show "0". In other words, not charging or discharging. A more meaningful indication is a DC voltmeter. But even a voltmeter is a little superfluous so most cars don't even have these, relying instead on the proverbial idiot light. Since we're not idiots, we need to add a voltmeter (if you don't already have one) to be safe and not stranded with a dead battery.
If the voltage doesn't stay above 13VDC or more while you're transmitting, you might not have enough reserve power for your rig. The left photo shows my voltmeter while I was key-down with 500 watts out and the engine at 2,500 rpm. The right photo shows the same key down condition except the headlights and air conditioning are on and the engine is idling. It wouldn't take long at this power level to drain the battery. Fortunately, most miniature radios shut down when the voltage drops below 11.6. Incidentally, at highway speeds the voltage remains ≈14 even with the lights and air on. This is possible because my vehicle is equipped with a 130 amp alternator. Yours may not have one this large so a voltmeter becomes especially important if you run high power.
Finding out the size of your alternator can be problematic. Sometimes you get lucky, and the amperage is written on the outside of the unit. This is true of most Denso, Akia, Nippon, and Bosch units. American made units are a mixed bag. Your dealer's parts department is a good source in case yours is not marked.
Because we typically don't run all of our accessories at the same time, there is usually enough capacity left over to power even a moderately powerful amateur transceiver. In some cases, a lot more. Enough, in fact, to operate a 500 watt mobile amplifier if we're careful with our electrical accessory use. Determining if you have enough capacity isn't all that difficult if you use some basic logic. If your car has a rear window defroster, you have about a 30 amp reserve when it is not in use. This is enough for any of the late model 100 watt transceivers like the FT100, FT857, IC706, IC7000, and even the 200 watt TS480.
If you use an amplifier, you'll need even more reserve. At 500 PEP watts out (≈1,000 watts input), the peak amperage draw is about 100 and the average around 40 to 60 amps including the transceiver. This requires a reserve of at least 70 amps. If your car has heated seats and mirrors in addition to the rear window defroster, you might have enough. In any of these cases, a good voltmeter is a valuable asset as long as you pay attention to it.
Just for the record, most of those in-dash-mounted voltmeters aren't very accurate. If you are attempting to rely one one, I suggest you check its accuracy with a known-accurate DVM. The voltmeter shown in the above photos is a Martel two-wire unit (read that as easy to install). Its current draw is under 2 mils, so may be left connected even for extended periods of time. The part number is QM-100V. It is about $45. Martel also sells similarly-sized hour meters, for those who want to keep track of their equipment on time.
Alternator ratings are on the increase, as electric motors replace belt-driven accessories like power steering, power brakes, water pumps, and even air-conditioning. This may sound counter productive, the fact remains that doing so reduces the parasitic loads belt-driven accessories innately exhibit. Add in EIS and the need for battery rapid recharging, and it is not uncommon for production alternators to be rated as large as 250 amps.
You don't always know what you're getting when you buy a new vehicle. Vehicle manufacturers know the alternator will only be delivering its full output for short durations, so they cut every corner they can. It is not uncommon for a 100 amp alternator to have a continuous duty cycle of less than 60 amps. Under the extra load imposed by high power mobile applications, the alternator and/or the interconnect wiring may over heat. This is especially true of low content (minimal accessorized) vehicles.
If you're contemplating purchasing a new vehicle, consider purchasing a heavy duty electrical system if one is available. The big three all offer heavy duty electrical systems on mid to large size vehicles (and some compact ones), and universally on trucks. The up front premium is small, usually under $100, for which you get a bigger, heavier duty alternator and a larger battery. As an alternative, order a trailer towing package even if you don't plan to pull a trailer. You typically get a solidly mounted hitch from which you can mount an antenna if you're not a hole driller; a transmission and/or oil cooler; and a bigger alternator and battery for one relatively low price.
Another good Internet site for really big amperage demands is Alternator Parts. They both offer a variety of different types and manufacturers. Some of their offerings will supply up to 500 amps, and no one makes a more powerful standard-sized alternator. They even sell a stand-alone, fan-cooled, rectifier package allowing a standard OEM alternator to safely handle more amperage. However, retrofitting a larger alternator gets very difficult on vehicles manufactured after ≈2004. This is due, in part, to the presents of an Electronic Load Detector (ELD) used on most vehicles made after that date. If in doubt, contact Alternator Parts and ask.
Lastly, talking on the radio while in heavy traffic should be discouraged due in part to the distraction it causes when your full attention should be on safe driving. Further, air conditioning, cooling fans, headlights, and slow engine speeds all add up to low alternator reserves. When in doubt, error on the side of safety, and hang up the mic.
Heavy-duty wiring systems are sold under a variety of names. These so called 'Police Packages' are a bit of a misnomer, because most of them cannot be ordered by us civilians as it were. However, they're also called Taxi service packages, or as Ford calls them, Modified Wiring Upfit Packages. In Ford's case, there are three fused power circuits, and two dry circuits with access to the engine compartment. They're not large enough for an amplifier, but they're adequate for up to 200 watt radios like the Kenwood TS-480Hx. The package also includes a bigger alternator and battery. Better yet, most Upfit packages include a predrilled and wired 3/4 inch hole in the roof. Though meant for signage, they're perfect for installing an NMO mount.
If you think you have alternator whine, it should sound like this. Whine can be caused by a large spike in the AC component as shown in the oscillograph at left; a very rare occurrence nowadays, and one which typically turns on the MIL (Maintenance Indicator Light). This said, almost without exception, alternator whine is caused by a ground loop (another reason to properly wire your installation). In most cases the whine is only apparent on the transmitted signal which is another indicator of a ground loop problem. If this is the case, chances are the cause is the use of a mag mounted antenna, or a poor RF ground return (open coax shield connection).
A related issue to alternator whine, is RFI generated by the diodes themselves. It sounds a lot like ignition and/or injector RFI, so it is difficult to diagnose correctly. You almost never have the issue with late-model stock alternators, but it seems to be the norm with cheaply-built, aftermarket alternators. Again, it pays to purchase a heavy-duty electrical system when they're offered (typically included with trailer towing packages as noted).
Recently, several manufacturers have started selling power cable filters, sometimes referred to as brute-force filters. They're advertised to cure alternator whine. The truth is, they only mask the real problem. If you have to resort to such devices, it is a sure sign you didn't wire your installation correctly, or you're using a mag mounted antenna. Worse, brute force filters add about .5 volts of drop (perhaps more), no matter how big and ugly they are!
One popular myth for curing alternator whine is to tightly twist the radio's power cable with an electric drill. Pundits often mention the fact that CAT5 cable pairs are twisted. While the technique does work well for balanced circuits, power cables feeding amateur gear is not balanced! This said, if twisting the power cable reduced some specific AFI or RFI issue, it is a telltale sign the power cabling was (is) inadequately sized!
Several companies sell a power lead filter which consists of a small ferrite core with 3 to 5 turns through the core. They're touted to cure all sorts of maladies including alternator whine. The truth is, they're a waste of money, as the very best of ferrite material is nearly worthless below about 1.5 MHz. They might be useful for keeping switching power supply hash out of a transceiver, but if the power supply really is that noisy you probably should replace it, not apply a band aid to it.
There is a lot of confusion about which type of auxiliary battery to use in a mobile installation, and some even question if one is needed at all. If you run a nominal 100 to 200 watt mobile transceiver, you probably don't need one, unless you're operating without the engine running—portable operation in other words. If you are operating as a portable, then the highlighted article is for you.
For those of us who run high power, an auxiliary battery is almost a necessity unless you wish to use $5 per foot welding cables for the inter-connections. For those who do not understand this logic, read my articles on Amplifiers, and on Wiring. It is basically related to I2R losses and minimizing IMD products.
The preferred auxiliary-battery type is an AGM (Absorbent Glass Mat), and there are several reasons why they are. The most important one is, they don't outgas unless they're abused (overcharged for example). What's more, unlike a flooded battery, an AGM can be mounted in any position, even upside down! This said, any auxiliary battery should be installed in a battery box, and properly restrained. Doing so, also prevents accidental shorting of the exposed connections. The rule of thumb for battery restraints is 6Gs lateral and 4Gs vertical. The last thing you want is a 60 pound battery flinging acid all over the insides of your vehicle!
Auxiliary batteries used in high-power applications should be SLI (Starting, Lights, Ignition) types, like the Optima RedTop® shown at left, or the Exide Orbital® shown at right. Remember, this application (amplifier peak current support) is high amperage for short durations, and not long-term reserve capacity like you would need in a portable application. Since both batteries are lead-acid (AGM or otherwise), the batteries may be connected in parallel. In fact, using an isolator on such a set up defeats the purpose which is to keep the voltage as stiff as possible. Quite obviously we need to isolate them with fuses in case the wiring gets shorted.
Don't assume circuit breakers are the answer to fuses. Circuit breakers cannot handle instantaneous currents much above 2,500 amps, and some cannot handle 1,000 amps! Under direct short conditions the contacts in a circuit breaker will weld together with obvious catastrophic results!
Here's another important point to remember. Batteries designed for marine applications are not the battery of choice for any mobile installation, the fact they have screw terminals notwithstanding. A battery rated for marine use is designed to maintain at least an 80% SOC after sitting uncharged for 12 months or more. They are a form of SLI battery, but typically have less starting amps and less reserve power than a true SLI. Incidentally, the terms Marine and Deep Cycle seem to be synonymous terms at least in the amateur community. They're not, even though some battery manufacturers would have you believe otherwise.
There are batteries designed to be discharged lower than 50% SOC (state of discharge), yet maintain a reasonable charge-cycle life (≈150-200). This is not the type of battery you want to use, unless you're operating portable. Even then, they have to be sized based on their duty cycle. In the case of high power mobile, it is the peak current capability of an AGM battery that is ideal for the application.
Fully charged, the nominal resting voltage of a lead-acid battery is 12.2 to 13.1 depending on construction. By construction I'm referring to the plate construction, and the electrolyte type (liquid or gel). Standard car batteries are referred to as "flooded" in that the sulfuric acid electrolyte is in liquid form, and the plates are usually flat. This is true of most OEM batteries, (gasoline or diesel). The only exception are hybrid vehicles.
All lead acid batteries generate hydrogen gas during normal operation, and becomes excessive during overcharge conditions. Hydrogen gas is very explosive, and even a minor spark can ignite it. Any resulting explosion isn't a pretty sight, as the electrolyte is sulfuric acid! Since the gas is vented to the outside, flooded batteries shouldn't be used in enclosed areas like the trunk of a vehicle. AGM batteries outgas too, but the hydrogen gas is absorbed by the glass mat. Here too, overcharging can cause more gas to form than the mat can absorb. Thus manufacturer's maximum charge rates shouldn't be exceeded.
A typical lead-acid battery has an internal resistance at full charge of about .003 ohms although some types are slightly higher, and some slightly lower. Under direct short conditions, the maximum current can exceed 3,000 amps, and a decent quality AGM, almost 4,000 amps! Doing so can cause some batteries to self destruct, hurling sulfuric acid far and wide, so handle them accordingly! It is best to keep their plastic post caps on until you actually make the connections. When removing them, or installing them, the negative lead should be removed first, and installed last. Why? Think about it!
If you have about 3 hours of spare time, and you want to know more about battery technology than most engineers, then visit Battery University! Better yet, the ARRL sells the third edition of the book the site is based on, Batteries in a Portable World, by Isidor Buchmann. If you're into batteries for any application, this book is the definitive source.
Mixing Battery Types
It is not recommended to mix battery types (i.e.: lead acid interconnected with a lithium iron phosphate), even if a battery isolator is used. The reason is simply that every battery type has its own charging parameters, as discussed on the Battery University web site.
Although lead acids have cold weather limitations, some battery types are even less capable. For example, battery manufacturers currently guarantee lithium iron phosphate (LiFePO4) cell capacity only down to approximately -13°F (-25°C). Lithium-yttrium (LiFeYPO4) cells (lithium-iron-phosphate cells doped with yttrium) enable operation down to -31F (-35°C). While extreme cold weather isn't a limitation in most amateur installations, the fact remains alternative battery types require some very special considerations, not the least of which is a high procurement cost.
For example, Smart Battery Corporation manufactures a lithium-iron-phosphate battery system, designed to directly replace a lead acid SLI battery. Because of the necessary electronics which assures equal charge balance among the four-cells, and 50 Ah unit sells for nearly $700! This high cost is partially offset with a few advantage. At 15 pounds, the battery about 75% less than an equivalent Ah lead acid. The output voltage (≈13.2 volts) remains fairly level up to about a 10% SOC. In any case, consultation with Smart Battery before purchase would be a prudent undertaking.
Few people realize there are literally hundreds of different types of vehicle batteries, and thousands of variations—size, post styles, post placement, flooded, gel, you name it. If you're interest, here is a web site worth looking over.
The only time batteries need to be isolated in a mobile application (other than RVs) is in portable operation. Their use in high power applications should be discouraged for several reasons, not the least of which is SOC (State Of Charge) considerations. Simple diode isolators will always have forward voltage drop of about 1 volt, and they can also play havoc with the charging circuitry in some vehicles, leading to illuminating the MIL (Maintenance Indicator Light). This leads some folks to use isolation relays, and they too have their drawbacks. But there is one brand of isolator which combines the attributes of both, and that is the one made by Hellroaring®.
The Hellroaring uses diodes and FET switches in its design. It is also remotely controllable. This fact allows all of the batteries (two or three) to be combined if necessary. It is competitively priced, and available directly from the factory. If you just have to use an isolator to stay warm, and fuzzy, this is the one to use.
Perfect Switch® also makes isolators and switches for high current applications, and both employ FET technology. One of their units is shown at left. One very good advantage is there are no contacts which could fuse together in a dead-short scenario. In fact, drawing current over their rating will cause them to disconnect, and require a reset. This is about as fail-safe as you can get. Proper fusing is still required, however.
Solenoid relay type battery isolators are available from a variety of suppliers. The one shown at left is a model 1314-200 from Sure Power® division of Cooper Industries, better known by their fuse line moniker, Bussmann®. Electronic circuitry controls the engagement of the solenoid based on the voltage differential of the main and auxiliary battery, but can be controlled manually.
Just for the record, a number of these units shipped to Australia and the European Union between 2009 and 2011, had defective capacitors which can cause the unit to overheat, and potentially catch fire. Information on the factory recall is on Cooper Industries web site.
Lastly, most alternator circuits incorporate a fuse. If you suddenly connect a fully discharged auxiliary battery to the charging circuit, it is possible to draw enough current to blow this fuse. Obviously you should keep a spare fuse on hand, and you should also follow Hellroaring's recommendation about delaying the FET closure until the current and voltage stabilize.
There are a couple of important items to keep in mind when using any isolation technique. First, most automobile manufacturers use some form of BMS (Battery Monitoring System). Battery and/or alternator current and/or voltage levels are used as data inputs to the engine control computer (see the Wiring article for more information). Suddenly connecting a second battery can cause fault codes to be written to the OBD II memory, which will turn on the Maintenance Indicator Light (MIL). It can also cause the main battery fuse (≈120 amp fuse) to blow. In any case, you should carry a spare. Incidentally, the battery fuse in most modern vehicles are OEM proprietary, and usually contains part of the ELD (Electrical Load Detection) circuitry (Hall device). Read that as expensive!
Almost no matter what you do (battery isolator use notwithstanding), eventually there will be a differential in battery voltage between the main (SLI) battery, and an interconnected second battery. The causes are a bit esoteric, but are due mainly to small resistances in the wiring, fuse holders, the fuses themselves, and even the connectors. While one wouldn't think a few milliohms (thousandth of an ohm) could make a difference, indeed it can. It is for this reason that wiring maintenance should be routine.
All connections should be checked to make sure they're tight, not frayed, corroded, worn, or showing signs of overheating. Battery connectors should be checked with a DVM between the battery post, and the battery clamp even when they look perfectly good. Here is how you do it.
First, never use an ohmmeter, digital or otherwise! After all, the connections are under power! Rather, set your DVM (analog meters are not accurate enough) to auto or its lowest voltage setting. Measure across connections. That is to say, between battery and the clamp, across a fuse holder, or any other connections that is screwed, bolted, or clamped together. Any reading over about .015 volts is excessive!
If need be, any connection should be cleaned and/or retightened and/or reclamped to reduce the voltage differential to about .01 volts per connection! Yes! It is that important to assure long battery life, and good performance from your mobile!
In order to maintain a solid 13.8 volts to operate the radio, a lot of amateurs opt to use a Battery Booster. Known by at least a dozen names, they act like a switching power supply, and although the battery voltage drops, the output remains steady. The one shown at left is a W4RRY unit, and the one below right is the MFJ unit. By the way, the November, 2008 issue of QST has a product review on these units including one made by TGE.
I should point out, TGE has several new battery boosters. These include a 40 amp (shown below right), an 80 amp, and a brand-new 120 amp unit! All are mounted in aluminum cases. It is interesting to note, that the 120 amp unit is capable of boosting even the largest of mobile amplifiers, including the SG500, plus the current load of the driving transceiver.
Most of these units include a low voltage cutoff, but some don't which can lead to problems. As stated several times above, any nominal 12 volt lead acid battery is considered discharged when the voltage drops to 10.5 volts under load. Discharging them lower than this will drastically reduce the life of the battery. Without low voltage protection, the typical end result can be a ruined battery.
Incidentally, none of the current battery boosters have over-voltage cutoff.
The question remains; is a battery booster is needed? There is no clear-cut answer. Certainly for portable operation, they have a definite use. However, in most mobile-in-motion operation, where the wiring is correctly sized, and the alternator is of adequate amperage, their use is questionable. There is also an issue with respect to battery monitoring systems (BMS), in that drawing the battery voltage down past a preset point, can cause the MIL to illuminate, and a code being written to the OBDII. There is also an issue with cost if you run an amplifier as the 120 amp TGE unit is over $500. With adequate wiring and charging circuitry, the need is perhaps moot.