Which transformers do you recommend and what component next to it are necessary? The cut-off frequency is 40kHz, and the load resistance is 4 ohms because we have a 4-ohm speaker (the values used here will also work with an 8-ohm speaker, but it is best to adjust the filter according to the speaker you choose). the red cells show the headphones with these impedances should not be connected to the output terminals directly as there is a serious risk of drivers being burned/damaged/blown. Balanced amplifiers basically have 2 amplifiers which have the same signal on it but in opposite phase. There are two of them: One as an input, one as an output for the speaker, although it is better to connect the speakers direct to the power supply ground, to remove some humming noise. When it has a TRS out I don’t know how that will be wired. With this information we can calculate the values of the inductor and the capacitor: \[L = \frac{4\sqrt{2}}{2\cdot \pi \cdot 40000} H = 22.508\mu H\], \[C = \frac{1}{2\sqrt{2}\cdot \pi \cdot 40000\cdot 4} F = 0.703\mu H\]. output power due to current limiting of the amplifier design. On second amp they actually sound quite decent from hp out (JVC A-X2). That's it. thank you. published: Apr-5-2013, updated: Aug-31-2019. Welcome to TubeDepot Javascript must be enabled to use this site. 2pcs Classic Version Tip41c Jlh1969 Single-ended Class a Power Amplifier DIY Kit $13.89 New 2 X 8 Watt Class D Bluetooth 4.0 Audio Amplifier DIY Kit With Volume Knob - TSA (2) The red (or +) connector of the amplifier must be connected to Right + (and for the left channel the Left + and the black (or -) connector of the amplifier must be connected to Right – (and for the left channel the Left –). Dear Frans, that’s quite some good info, thanks for that! A lot of D.J.- and professional monitoring headphones can have (and may need) such power ratings as they are sometimes used as little speakers hanging around the neck or lying on a console while playing loud acting as small desktop speakers. You are better of using either KiCad (Which is open-source - free and easy to learn) or start a new project with Eagle. I am trying to build one myself and I have a few issues. When the same signal is sent out balanced the ‘other’ amp that is now connected also will have a 1V output signal but in opposite phase. If me measure "+12V", on the multimeter it reads +12V. This effectively ‘parallels’ the two resistors that are used. It should be noted that most power amplifiers can deliver a HIGHER voltage in reality than the one given here because of the substantial load (4 – 8Ω speakers) the speakers provide is absent and thus the often unregulated internal power supply voltages do not drop allowing for a somewhat higher voltage swing. To remove the hum noise (50/60 Hz, from the mains frequency), I used a star-ground configuration; this means connecting all grounds (amplifier ground, signal ground, and speaker ground) at the same point, preferably on the power supply PCB, after the rectifier circuit. I went over the whole circuit several times to make sure everything is connected properly and it seems to be. It can NOT be used with single ended (3 wire) headphones. Hi, At 300ns response time, it is not the fastest and can definitely be improved but it does the job. The input signal has its own connector and there are two spade terminals for ground: one for the power supply and one for the speaker. EL34 Audio Stereo Tube Integrated Amplifier Single-end Class A Power Amp DIY KIT. Because of the many possible configurations and connectors such an attenuator has to be custom made. In class B and AB modes, the output stage operates in a pushpull configuration, where one set of output devices delivers positive… The rest of the capacitors in the design also need to have an appropiate voltage rating. R1 = 33Ω (5W) and R2 could have values between 10Ω and 3.9Ω (3W to 5W) depending on how much attenuation you want/need. Lately they have kindly printed projects that I had already posted on the web, but I decided that … The power amplifier takes the high impedance input signal, further amplifies it and transforms it into a low impedance signal, suitable for the speaker. That should give you 1V at max output power level. Power amplifiers can deliver enough voltage. Thanks for your knowledge and have a great day. Power = voltage x current so the power is 2 x 2 = 4 times higher = 128mW in 32Ω. The HE5(LE) is rated at 2W and the NAD can deliver 5W (non clipping sinewave) so take care you don’t turn it up all the way to see how loud it can go. The load the amplifier ‘sees’ is a bit lower as the R2 is in parallel to the impedance of the headphone. When unsure do NOT connect the ground (-) connections of these amplifiers together. At the time, he wrote: “I feel that it’s important to support AudioXpress, a magazine with which I have a 35 year history, and which also serves as a mainstay for the DIY community. Below the table for 3W to 6W rated headphones. Below the universal schematic for a balanced headphone amp attenuator. The same way the regulators in this circuit are being used to produce "non 5V" power rails. There is, however, a cheap and easy ‘fix’ so most headphones can be connected to power amplifiers but NOT directly. DIY Mini 12Volt Power Amplifier Editor Elcircuit Published Saturday, April 21, 2018 On this occasion, I will share a mini power amplifier with a power output that is not big enough, and this power amplifier can be supplied with 12volt voltage up to 24V asymmetric. With this simple trick the output voltage of the amplifier is lowered by voltage division, similar to what is described above, BUT because 2 resistors are used we can lower the output resistance ‘seen’ by the headphone. Adding NFB and making it work might be a worthwhile design exercise for a student, but if you just want to listen to music, there are other proven class-D amps out there available as chips or complete modules, ready to use for less than the price of a Happy Meal. There is a catch here which is that unlike ‘normal’ 3-pin headphone plugs (The so-called TRS Jacks) which regardless of size (2.5mm, 3.5mm or 6.3mm) have a pretty standard configuration. The amp has enough power for medium to high efficiency speakers at normal listening levels. I used IR2113 as a direct replacement for IR2011. Somewhere between 120-140W. I'm not an audiophile and not an expert on amplifiers either. It needs to be iron powder; ferrite can work but it will need a gap or it will saturate. This means that the signal that we want to achieve will not be attenuated too much. Subjectivist, Objectivist or Inbetweenivist ? The table below is for the same types of headphones (200mW) but with a series resistor of 120Ω (3W rating). A 32Ω headphone on a 40W/4Ω amplifier can receive 5W, way too much for drivers rated for just 0.2W. Would any male 1/4 to female 1/4 attenuator work? The diyAB "Honey Badger" Class AB Power Amp - 150W/Channel Impressive piece of kit I was impressed by the quality of the components and the chassis. My interior sound card with HP amp also has output levels of 3.0V. Certainly NO problem when using a power amp to drive headphones. The there is the question do we really need deafening levels when the volpot is at maximum setting ? The table above shows it is no problem to connect high impedance (> 300Ω) directly to the output terminals of amplifiers capable of delivering  50W into 4Ω, Headphones with 600Ω can even be driven safely by 65W/4Ω power amps. On integrated amps: on one they also lacked bass, power was there (Denon PMA700V, 100wpc/8ohm). The 4-pin XLR is not used that much in audio but is gaining in popularity for balanced headphones as you need just one (professional quality) connector. It’s easy to see these headphones are not easily blown up but it should be noted most planar magnetic drivers are somewhere between 32Ω and 60Ω in general. The mono plug only has a sleeve and tip and is often found on the end of a microphone. My point is, attenuation for older amps might be needed not only on output, but on input too, as amp might reach it’s rated power output with volpot still in sight of -∞ mark. Shouldn’t it be the other way round? Above on the left there is the well known TRRS jack (usually 3.5mm) which is found on many headphones these days. Other headphones may become boomy and ‘fat’ sounding. Since the impedances of headphones are higher than those of speakers headphones need less current so all power amplifiers have absolutely no problems to provide the needed current. The output can be 25 ohm impendance, no problem, you would just (again) need to adjust the output filter accordingly. This is because the 2 resistors not only divide the voltage so it is lower but also create a lower output resistance. When you will finally hear that crisp sound coming from your speaker, it will all be worth it. For the MOSFET driver, I chose to use the IR2110. As you can see even low power amplifiers can potentially damage these headphones as the biggest part of the table is red. In theory, an op-amp can be used as a comparator, but in reality op-amps are designed for other types of work, so make sure you use an actual comparator. For low power amplifier, I think a different design would be better. A factor 3 in voltage reduction = -10dB will be sufficient to protect and drive most headphones out there. so when In case of doubt or other questions feel free to contact me (Solderdude) in this thread in our FORUM. For home amplifiers this number usually starts with 8 ohms. All you need to add is an enclosure with the proper input and output connectors, power … R1 and R2 for both the left and right channel are mentioned in the tables further down on this page. Just fire up that soldering iron, etch your PCB, and start working. The drawing is from www.tubecad.com which is a great source of info about amplifier designs. You should use a bipolar power supply with ±30V rails. I’ll be using same design with appropriate component values. 77 $11 99 When soldering wires onto these plugs you must realize what the pin numbering is on the solder side (mirrored from the plug side !). Could be less. Is there anyone with some experience in this issue that can help me out? An alternative is the IR2011, which is used in the reference design. These MOSFETs have low gate charge for faster switching and low RDS(on) for lower power consumption. I just had a cap blow in my face for the first time ever after connecting the grounds together! This whole area is excellent but is it readily ‘discoverable’ to newcomers? The pins (male connector) are all equally long but in the socket (female) the 1 socket is slightly longer. 5W peak power in real music usually means average power is below 0.5W. It's not like measuring audio performance requires specialized instruments from Brüel & Kjær or Sound Technology these days. for an HE5. Is this a common problem? To find out why read resistance, impedance and other issues. This is an informative article & many thanks for posting it. It is best to choose something between 40 and 60 kHz. how about a nice power supply project along with a simple enclosure to complete the package?! I wouldn't go lower than 20-24V for the power supply ,but at least 30V is recommended. Ah!, I’d forgotten about it being a separate area. If you have any trouble with your build, comment here or post on the forum using as much information as possible. It is based on the IRAUDAMP1 reference design by International Rectifier (Infineon). You are right that they will not be stable in regards to 0V, they will, however, be stable in regards to the negative rail, which is how the IR2110 is referenced. It is obvious the higher impedance headphones can be connected directly to amplifiers that can provide lots of power. HI IS IT NECESSARY TO HAVE 220N AT +TO G AND -TO G ??? I checked and the guys at Infineon (IRAUDAMP1 reference design) use the same type of notation for their power supply. For some reason I keep getting the notification emails in my spam inbox. That is a very good ideea. This looks great. Your email address will not be published. On the reguatlor you have got 18 volt on the input and 25 volt on the output. You do have a valid point. The output signal of the Left and Right channel thus are NOT connected like in normal headphone outputs. First of all, I named this amplifier Luke-The-Warm because the heat sink only barely gets warm, as opposed to a Class AB amplifier, whose heat sink can get quite hot if not actively cooled. You could use the IRF640N, but the RDS(on) is significantly higher, leading to an amplifier with lower efficiency. Should you hear background noise or can only use the bottom part of the volpot range (unlikely as the efficiency is very low) then you can always add some resistors. This is standardized and all XLR sockets in (pro) audio equipment is usually connected that way. For lower impedance headphones (some of them are rated just 0.05W) attenuation is recommended as well as for usage with IEM’s . Or might you have a better suggestion? Most (balanced) high-end equipment often uses this plug. It may be wise to use higher power and very low resistance value attenuator resistors that, when combined create a resistance close to the impedance the power is rated in (4, 8 or 16 Ohm for instance) because of the used transformer expecting a certain load. Something similar happens when you try to add negative feedback to improve stability, bandwidth and THD, I need to determine the feedback gain (and with that the total gain) by design so that I can then choose the value of certain components. When the load decreases, the amplifier's output increases. The observant reader is seeing rather high output resistances. The main difference is that instead of ΔΣ modulation, mine uses PWM. Also I don’t see a potentiometer for change master value. For the sake of illustration below a table for a 680Ω (5W rated) series resistor. It would be possible in theory if you use the rectangular signal before the filtering (the last inductor and capacitors), which can be used with a transformer, but I do not know after that what needs to be done. Does this sound safe/correct to you? A PWM of 200 kHz is allready very high to operate with these devices. Finally the filter. Because heavy attenuation can cause tone loss, I have included a bright switch to help compensate for the loss in treble. If we want to put the previous block diagram into practice, we will stumble upon some problems. An input signal of 4.6Vmax would be enough for the full output swing. You need to find out what pinning is the correct one for the headphone AND is present on the amplifier/source. HiFi Class AB Tube Power Amplifier DIY Kit Push-pull Stereo Audio Amp 12W+12W. Because we need two outputs from the comparator, one for the high-side driver and one for the low-side driver, I decided to use the LM393AP. The quality factor \[Q = \frac{1}{\sqrt{2}}\]. Get the BOM. In this case you need a TS (Tip-sleeve) connector to the amp and make it mono (TRS) for the headphone. Degraw DIY Speaker Kit - PAM8403 5V Amplifier + 2Pcs 4 ohm, 3 watt Speakers - Mini Class D Digital Audio Amplifier amp Board Module kit for Arduino, Includes 3.5mm Plug! That’s great to know Frans. With it you can drive high impedance headphones (300 Ohm) and most planars directly without the need to attenuate. Don't worry if it isn't perfect—just make it tight. What’s missing is voltage divider networks and still have to figure out how to ‘present’ is due to the many variables involved. No, When the amplifier used is of a so called ‘bridged’ design, such as a lot of class-D and car-audio amplifiers, unless 4 wire headphones are used. The cut-off frequency is calculated at -3dB, so we want it to be a bit higher in order to not filter sounds that we want to hear. the headphones range from 32 to 250 ohms. Drawing more power than the amplifier was designed for will damage the amp. No, because most low impedance headphones run a a high risk of being burned to a crisp when left unattended and the volume is accidentally turned up. In other words which signal(s) should go on which pin(s). All connections are 100% correct even though my PCB layout differs slightly. In this circuit, the regulator's ground terminal is connected to -30 V; thus, the output is at -25 V, because -25 V is 5 V greater than the ground voltage. It is better to use a converter IC directly like the LTC6992 https://ibb.co/zm1s04H . A positive regulator can be used because the input and output voltages, which are labeled as negative in the schematic, are actually positive relative to the voltage at the regulator's ground terminal. This last thing i mentioned would imo be quite important addition to your truly great article: alot of people will probably test this on “old / vintage” integrateds. The most common connector is the TRS jack (also in 2.5mm, 3.5mm and 6.3mm). R1 = 33Ω (5W) Depends on the frequency, but keep in mind that this is an amplifier designed to go well with frequencies under 20kHz. In-line attenuators can certainly help here but doesn’t change the maximum allowable power in the headphone which is what the article is about. Any higher than this and we will run into trouble because the comparator and the MOSFET driver are not the fastest devices. Yes, because some ortho-dynamic headphones need a lot of ‘power’ which can be delivered easily with power amplifiers. Theory is one aspect and practice is another. I have a Sony subwoofer speaker unit with 2 ohms and 180 watts RMS (Aluminium tube -dual speaker -internally wired parallel)  .Can I use your circuit for this speaker unit?.If so what changes in this circuit I need to do ? (Meaning that I want to use this as a subwoofer amplifier). How can I convert this design into a constant voltage (100V),high impedance amplifier ? The thing is that class d has efficiency advantage depend on your need. Ugh, i completely missed the fact about noise floor going down with attenuator(s). Hey Cezar, I had a few questions about this project: I am trying to build it at home. The speakers are either KEF Q150 8 Ohms (min.3.7 Ohm) 86 dB ( 2.83V @ 1 m ) or LS50 8 Ohms (min.3.7 Ohm) 85 dB ( 2.83V @ 1 m ). I use al parallel 8,2 Ohm Mundorf resistor for each channel. Brilliant – thanks a million! Now we know what the input and output signals are we must find out which connectors are used and what their pinning is. I have fabricated -20 dB inline attenuators (simple two resistors, this link http://www.uneeda-audio.com/pads/ ). Many thanks in advance! Before other people like to try this with their amps I strongly recommend against this as headphone amps are usually only designed to deliver low power, certainly in low impedances. I would suggest to operate with the LM5104 for the half bridge driver together with the STP16NF06 NMOS transistors to operate at 500 kHz. If I want to to build an amplifier in the 20 -  30 watts range, what changes should be made to the circuit? The rectangular signal is amplified, and then a low-pass filter results in a higher-power version of the original analog signal. Amplifiers of 40W/4Ω can safely drive all ‘normal’ headphones and if we include the ortho dynamic headphones the whole table would be green. Very interesting, thank you. It does not matter if it does not work on the first try. Also go to the tdpri.com DIY Amplifier Forum and look at similar amp builds. Free shipping. If we measure the real ground (which is 0V), on the multimeter digit we would read +30V. Happy to share some brochures or construction manual incl. If the signal is 0v and the triangle wave oscillates between +/-5v a 200KHz square wave is outputted from the comparator. My email is johnjol399@aol.com if you'd rather email me. Hello john12, really you can't get the voltage value at the HO of IR2110, unless you connect the output MOSFETS, remember its a floating ground at VS, HO voltage can be achieved when the Lower MOSFET turns on. I know nothing about homebrewing audio gear, but this DIY 300W power amp, built on six LM3886 chips, sure looks bad ass. We measure the electric potential difference, V2-V1. This Class-A Push-Pull Tube Power Amplifier uses a Pair of Push-Pull Class A, Ultra Linear Mono Block Tube Amplifiers that can be used with several different vacuum tubes including KT77 / 6L6GC / KT88 with a 12SL7 driver and 6NO30 tubes. I used this notation because we connect the COM and VSS port of the IR2110 to the "-30V" rail. Interesting fact: external usb sound card/mixer and Denon integrated both had 120 ohm resistors in series with +L and +R out on headphones. In fact Nelson's DIY endeavors are called "First Watt" because in his own words "The first watt is the most important watt". I look in this bit from time to time but finally decided to ask. The blue cell shows these headphones may NOT play at substantial volume any more (depends on the used headphone). Thanks for the great article Cezar, I have a question about a bipolar power supply here in the US I can only find a dual +- 20vdc, is there a project you can recommend for building a bipolar +- 30vdc power supply. The higher impedance headphones (>300Ω) can be connected to 100W amplifiers. As most of these aren’t specifically for headphones below a listing of the 4 main configurations of this TRRS plug. Thats still about 300mV, but i figured some music might be recorded not so loud (older music of course) so better to leave some “reserve” there. No different settings possible and an impedance of 8 Ohm i believe the 9W is rated with. What is a Class-D audio power amplifier? I’ve tested them on JVC speaker output terminals, there was loads of power, but stopped until i put some in line attenuators (at input). The amplifier is one of the simplest I have encountered and it gives out a decent sound. I have tried them on sound card that is rated to drive 600 ohm cans, on external usb sound card / mixer and some integrated stereo (speaker) amplifiers. Create one now. It's all about trial and error. The bigger the output power of the amplifier the higher the output voltage and also the higher the added resistance needs to be. There are also unexpensive devices with just 5 mOhm channel resistance in order to improve the overall efficiency. These amp build instructions from StewMac are very good: StewMac_15_Watt_Build_instructions WARNING : A tube amplifier chassis contains lethal high voltage even when unplugged --sometimes over 700 volts AC and 500 volts DC. The solution is to use a voltage divider that lowers the voltage. "Insane amount of detail, deep bass and crystal highs" - Starbender The picture below illustrates the principle. It would have to be a special. Can it be good, also to ampliy ultrasound? I have the AKG K240 Monitor (600 ohm). Yes, because high impedance (> 300Ω) headphones can be connected directly to power amplifiers without damage Yes, because some ortho-dynamic headphones need a lot of ‘power’ which can be delivered easily with power amplifiers. Uheadpone = U amplifier x 1/(((1/R2) + (1/Zheadphone)) / R1 + ((1/R2) + (1/Zheadphone))). The power input of the amp says AC 18V 50-60Hz MAX 1A and the PS input says 25W MAX. The DC300 is the only available amp not being used here. When your headphone only has a TRS connector then you can build the ‘normal’ attenuator and simply connect the – L & R outputs together to form the ‘common’ (sleeve) contact of the TRS plug. Yep those are valid points when it comes to usable volume control range. I’ll add this to my daily checks. But in order to fully understand how one works, I need to teach you all its nooks and crannies. Whenever I update or add something I make a note on the ‘home’ page. Hi, John. Here are some links : http://www.ti.com/lsds/ti/audio-ic/mid-power-audio-amplifiers-5-50W-product.page and http://www.st.com/content/st_com/en/products/audio-ics/audio-amplifiers/class-d-audio-power-amplifiers.html?querycriteria=productId=SC983 . This integrated circuit makes sure to add that dead time that I talked about in the previous section. Yes, because high impedance (> 300Ω)  headphones can be connected directly to power amplifiers without damage Cezar, By the argument you put forward, any variable power supply that uses, for example, a LM317 regulator would have a 1.25V output all the time as it is a 1.25V voltage regulator. This single module contains everything in one place for a 2-channel dual-mono amplifier (rated 250W into 4Ω, 180W into 8Ω, at 1% THD, 1kHz signal) including input buffer and power supply. Most of the newer Planar magnetic (Ortho dynamic) headphones can handle MUCH more power than normal headphones because of the way they are built. It is obvious low power amplifiers cannot damage the headphones any more and even a 15W/4Ω amplifier can be used with music signals. This signal needs to be similar to signal coming out from earphone out. For the triangle generator, I used an LMC555, which is the CMOS variant of the famous 555 chip. The amplifier would be embedded within a 2-way speaker. JVC on other hand has 220ohm resistors in series. Some manufacturers offer converters or conversion cables from one plug to another. Sorry to trouble you fine folks but I have no clue what half of this page means, but if one of you can tell me that would be fantastic, here is the link to the amp, https://www.monoprice.com/Product?p_id=611815 if for some reason the link doesn’t work, it’s the Monoprice 15watt celestion. I would suggest to do a search for "Class D IC" and you will find some integrated circuits from ST and TI that are great. The load the amplifier sees = R1 + 1/ ((1/R2) + (1/Zheadphone)) and the output voltage  of the circuit can thus be calculated as. They are just used to get a power rail that is offset by 5V from another rail. What have I to modify to have in output an 25 Ohm impedance? Hi, thanks for the post! Create a free website or blog at WordPress.com. In this case volpot will be very sensitive and users might actually drive amplifer into clipping and bad distortion. It is obvious there are many variables including the differences in efficiency the possible outcome of calculations would be too much to fit in a few tables. Also, I included a bypass switch for obvious reasons. Because the switching of the MOSFETs is not done instantaneously, but is more like going up and down a hill, the transistors' ON time will overlap, creating a low-impedance connection between the positive and negative power supply rails. The numbers are generally given for impedances of 4Ω or 8Ω (sometimes even 2Ω or 16Ω) but these power levels will not be reached in headphones as the drawn power is determined by the output VOLTAGE of the amplifier and the load (IMPEDANCE), the higher the impedance, the lower the current at a given voltage. The IR2010 or IR2011 as well as the comparator are relatively slowly devices. So I removed the MOSFETS and measure pulses at pins 1 and 7. Below a few possible pinnings of gear with a 4 pin TRRS jack connected. The monoblock tube amp kit uses an SRPP input stage with 5751 driver tubes and a push-pull output stage with KT88 power tubes. Which, so it seems now, was probably … How would i add a volume control knob to this circuit? Build Your Own Amplifier. 4x the power (= 2x the voltage) is an increase of 6dB in amplitude. I designed this amplifier for an output power of about 100-150W. Using the said toroid, wind 40 turns of 0.8-1mm diameter (AWG20-18) copper enameled wire. When loaded with 8 Ohm you will get 8.5V at 9W. You will need an attenuator between the speaker and headphone. Is it before the input of the amplifier? UcD and Ncore modules are well known to be one of the best amplifier modules available today. The circuit is described above. I am currently working on a design for school and have been looking for insight from various projects. Thank you very much for you input. Thus buy 2x 33Ω, 2x 10Ω and 2x 3.9Ω  for instance or values between them to try. Any risk involved in this method? I'm guessing there is a whole lot of distortion, since there isn't any negative feedback to compensate for all the imperfections in the triangle wave and comparators and output stage; it should be fine for signals with no dynamic range like a siren, or a compressed speech over a bullhorn. This basically means that the input is encoded into the duty cycle of the rectangular pulses. Sometimes the XLR socket is even combined with a TRS socket (see picture on the right). This is two comparators in one package, and we just swap the inputs for the second comparator. The input signal is converted into a pulse width modulated, rectangular signal using a comparator. The reason for that is we can say the output resistance of the power amplifier is 0Ω (or negligibly close to it compared to the impedances and resistances that are connected). A passive attenuator at the output lowers the amp noise relatively and prevents accidental overloads. Since the comparators at the input are powered by +/-5 V, why not also power the IR2110’s input with that and avoid the level shifter? Being a balanced 9W tube amp do you have any quick advice regarding resistor values or should I experiment a bit? can i use +-90 v supply? But there is other way to check it even though with out MOSFETS connected. An interesting article, and well done to help understand these amps. What is a Class-D audio power amplifier? https://diyaudioheaven.wordpress.com/ It varies greatly (100-150W) depending on your power supply. I would be the only one in this house trying this (no kids etc ).