On 10/12/2012 12:56 PM, Tim Wescott wrote: ... > I think that complex numbers can have some pretty deep mathematical> reasons behind them. > > But an engineer's _purpose_ in using them is as a convenience, rather > than as a whole field of mathematics that must be mastered fully before > proceeding, is going to lead to success sooner rather than later. > > I think you could do everything we do using complex numbers without ever > letting 'i' or 'j' enter into the discussion. But you'd be doing a lot > of twisting and turning and application of a list of rules as long as > your arm, instead of just using 'i * i = -1'.Tim is right. Consider a right triangle. For definiteness, put one acute angle at the origin and the right angle on the x axis. The length of one side is then x and the other side is y. The tangent of the angle at the origin is then y/x. What is the tangent of twice that angle? One can, with some tedium, show that 2tan(x) tan(2x) = -------------. (I had to derive that in high school.) 1 - tan^2(x) One can also express the hypotenuse, both length and direction, as x + iy. When multiplying complex numbers, their angles add and their lengths multiply. I'll use that very useful property here. Squaring a complex number doubles its angle, so lets do that: (x + iy)(x + iy) = x^2 -y^2 + i2xy. Then the tangent of the doubled angle is 2xy (2xy)/x^2 2*tan(x) tan(2x) = ----------- = -------------- = -------------- with far x^2 - y^2 1 - (y/x)^2 1 - tan^2(x) less tedium to the calculation. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
complex notation
Started by ●October 12, 2012
Reply by ●October 12, 20122012-10-12
Reply by ●October 14, 20122012-10-14
On 10/13/2012 10:47 PM, manishp wrote:
> Sirs,
>
> Few basic questions on DFT:
>
> 1) what is the signifiance of -ve amplitude in frequency domain
If I tell you that my car battery reads -13 volts, what does that mean
to you?
> 2) what is the significance when cosine component has -ve and sine
has +ve
> amplitudes
In typical phasor diagrams, the sine component is along the x axis and
the cosine component is along the y axis. That puts the signal you
describe in the fourth quadrant.
> 3) In some literatures, the frequency domain is shown with magnitude and
> phase. Shouldn't this be magnitude and phase for real and imaginary parts
> (so totally 4 components)?
Complex numbers can be described either with magnitude and phase or with
real and imaginary components. Using both is superfluous and confusing.
> 4) How is the energy calculated using Parseval's equation in the complex
> plane. Does it use real & imaginary and their phase counterparts for
> calculation also?
No. See above.
> 5) what is the purpose of windowing and whether this is done in time or
> frequency domain?
That is another topic. First, understand Euler's identity:
A*e^(i*x) = A*cos(x) + A*i*sin(x),
where A is the amplitude and x is the phase.
Jerry
--
Engineering is the art of making what you want from things you can get.
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Reply by ●October 14, 20122012-10-14
On Thu, 11 Oct 2012 23:27:32 -0500, "manishp" <58525@dsprelated> wrote:>Sirs, > >I have few questions wrt to complex numbers. > >1) I would like to know the main purpose of using complex numbers. > >2) I would like to know given a number in complex notation, is it possible >to convert this into a real number. > >Thanks, ManishCheck out: http://en.wikipedia.org/wiki/Complex_number I think you may have the same problem as I: Insufficient foundation in certain areas of math to ask the question for which I seek an answer! John Ferrell W8CCW
Reply by ●October 14, 20122012-10-14
Jerry Avins <jya@ieee.org> wrote:> On 10/13/2012 10:47 PM, manishp wrote:> > Few basic questions on DFT:> > 1) what is the signifiance of -ve amplitude in frequency domain> If I tell you that my car battery reads -13 volts, what does that mean > to you?That you installed it backwards, at least on any car that I know about currently. When I was younger, in the 1960's, my dad had a collection of Popular Science (1962 to about 1974) that I would sometimes read. One of my favorite to read was about Gus the auto mechanic. One story, "Gus and the Backward Battery" I still remember. You probably have to know some about cars in the 60's to understand (likely Jerry is one), but as the story goes one of Gus' regular customers comes by after jump starting his car that had an almost completely dead battery. Sometime later, Gus figures out what happens and goes out to chase him down to tell him not to turn off the ignition. Among the things reported when he came by the shop was that the car radio didn't work anymore. -- glen
Reply by ●October 15, 20122012-10-15
On 10/14/2012 7:20 PM, glen herrmannsfeldt wrote: > Jerry Avins <jya@ieee.org> wrote: >> On 10/13/2012 10:47 PM, manishp wrote: > >>> Few basic questions on DFT: > >>> 1) what is the signifiance of -ve amplitude in frequency domain > >> If I tell you that my car battery reads -13 volts, what does that mean >> to you? > > That you installed it backwards, at least on any car that I > know about currently. Do you know that the ted lead of my VOM isn't connected to ground? > When I was younger, in the 1960's, my dad had a collection > of Popular Science (1962 to about 1974) that I would sometimes > read. One of my favorite to read was about Gus the auto mechanic. > > One story, "Gus and the Backward Battery" I still remember. > > You probably have to know some about cars in the 60's to > understand (likely Jerry is one), but as the story goes one > of Gus' regular customers comes by after jump starting his > car that had an almost completely dead battery. > > Sometime later, Gus figures out what happens and goes out to > chase him down to tell him not to turn off the ignition. > Among the things reported when he came by the shop was that > the car radio didn't work anymore. I am reminded of the night I helped a buddy replace his VW's generator with one from a Karmann-Ghia. With only a little fudging, it fit. Everything looked good when I showed up, but it wouldn't charge. I went over the wiring twice and everything was in place, So I removed the cover of the voltage regulator and pushed in the reverse-current by hand. Even though I knew what was coning, the sparks made me jump. My buddy looked like he wanted to clobber me. I said to try it now, and he did, and it charged. He wanted to know what the fix was, but I was annoyed enough to tell him only that the generator turned the other way in its previous home. He eventually figured out why the fix worked. Jerry P.S. Solution on request. -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●October 15, 20122012-10-15
Jerry Avins <jya@ieee.org> wrote: (snip)> >>> Few basic questions on DFT:> >>> 1) what is the signifiance of -ve amplitude in frequency domain> >> If I tell you that my car battery reads -13 volts, what does that mean > >> to you?> > That you installed it backwards, at least on any car that I > > know about currently.> Do you know that the ted lead of my VOM isn't connected to ground?Yes, I wasn't so sure what you meant, but the usual way of measuring car voltage is relative to the frame ground.> > When I was younger, in the 1960's, my dad had a collection > > of Popular Science (1962 to about 1974) that I would sometimes > > read. One of my favorite to read was about Gus the auto mechanic.> One story, "Gus and the Backward Battery" I still remember.(snip)> > Sometime later, Gus figures out what happens and goes out to > > chase him down to tell him not to turn off the ignition. > > Among the things reported when he came by the shop was that > > the car radio didn't work anymore.> I am reminded of the night I helped a buddy replace his VW's generator > with one from a Karmann-Ghia. With only a little fudging, it fit. > Everything looked good when I showed up, but it wouldn't charge. I went > over the wiring twice and everything was in place, So I removed the > cover of the voltage regulator and pushed in the reverse-current by > hand. Even though I knew what was coning, the sparks made me jump. My > buddy looked like he wanted to clobber me. I said to try it now, and he > did, and it charged. He wanted to know what the fix was, but I was > annoyed enough to tell him only that the generator turned the other way > in its previous home. He eventually figured out why the fix worked.Trying to remember the Gus story "why" from about 40 years ago, the battery was so far discharged, that when jump started in the wrong polarity (I suppose it was a positive ground car) that the battery just recharged the other way around. (Lead-acid can do that, most others can't.) The field current also changed sign, so that the battery was now being charged in the new polarity. (Cars with alternators wouldn't do that.) But there has to be a relay to disconect the battery from the generator when it isn't running. (No diodes, like on an alternator.) As I remember it, that relay fused closed when charged backwards, so if the car stopped without disconnecting something the battery would discharge very quickly through the generator, likely with something melting. As I remember it, there were three relays in the voltage regulator, but I don't remember what they do. Besides the Popular Science, the story goes that one of the first books I read was the service manual for the 1960 Dodge that my dad bought (in 1960) when I was two years old. Well, maybe I mostly looked at the pictures. -- glen
Reply by ●October 15, 20122012-10-15
On 10/15/2012 3:07 AM, glen herrmannsfeldt wrote:> Jerry Avins <jya@ieee.org> wrote: > > (snip) >>>>> Few basic questions on DFT: > >>>>> 1) what is the signifiance of -ve amplitude in frequency domain > >>>> If I tell you that my car battery reads -13 volts, what does that mean >>>> to you? > >>> That you installed it backwards, at least on any car that I >>> know about currently. > >> Do you know that the ted lead of my VOM isn't connected to ground? > > Yes, I wasn't so sure what you meant, but the usual way of > measuring car voltage is relative to the frame ground. > >>> When I was younger, in the 1960's, my dad had a collection >>> of Popular Science (1962 to about 1974) that I would sometimes >>> read. One of my favorite to read was about Gus the auto mechanic. > >> One story, "Gus and the Backward Battery" I still remember. > > (snip) > >>> Sometime later, Gus figures out what happens and goes out to >>> chase him down to tell him not to turn off the ignition. >>> Among the things reported when he came by the shop was that >>> the car radio didn't work anymore. > >> I am reminded of the night I helped a buddy replace his VW's generator >> with one from a Karmann-Ghia. With only a little fudging, it fit. >> Everything looked good when I showed up, but it wouldn't charge. I went >> over the wiring twice and everything was in place, So I removed the >> cover of the voltage regulator and pushed in the reverse-current by >> hand. Even though I knew what was coning, the sparks made me jump. My >> buddy looked like he wanted to clobber me. I said to try it now, and he >> did, and it charged. He wanted to know what the fix was, but I was >> annoyed enough to tell him only that the generator turned the other way >> in its previous home. He eventually figured out why the fix worked. > > Trying to remember the Gus story "why" from about 40 years ago, > the battery was so far discharged, that when jump started > in the wrong polarity (I suppose it was a positive ground car) > that the battery just recharged the other way around. > (Lead-acid can do that, most others can't.) The field current also > changed sign, so that the battery was now being charged in the > new polarity. (Cars with alternators wouldn't do that.) > > But there has to be a relay to disconect the battery from the > generator when it isn't running. (No diodes, like on an alternator.) > As I remember it, that relay fused closed when charged backwards, > so if the car stopped without disconnecting something the battery > would discharge very quickly through the generator, likely with > something melting. As I remember it, there were three relays in > the voltage regulator, but I don't remember what they do. > > Besides the Popular Science, the story goes that one of the > first books I read was the service manual for the 1960 Dodge > that my dad bought (in 1960) when I was two years old. > Well, maybe I mostly looked at the pictures.By 1960, Dodge lightened the sheet metal considerably. My 1947 Dodge (bought in 1951) was built like a tank. I broadsided a police car that had run a stop sign, smashing the left rear door, removing the rear fender and leaving the rear bumper dangling. My grille remained intact. The disconnect relay that you cite is called a reverse-current cutout. I don't know why it could be expected to fuse, but as I wrote, it can make a big loud spark. It has both a voltage coil in shunt with the generator and a current coil in series with it. The way it works, the voltage on the disconnected generator builds up enough to pull the relay in on the voltage coil alone. When it pulls in, current flows to the battery through the current coil, increasing the field that's pulling the relay in. When the generator slows enough for the current to reverse, the series and shunt fields buck instead of adding, and the relay drops out. So why did the Karmann-Ghia generator work after I pulsed the cutout by hand? Hint: think residual field. Those DC generators needed not only the reverse-current cutout, but also voltage and current regulators. The three relays in the box performed one function each. An alternator needs at most a voltage regulator, and can get by without even that. How come? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●October 15, 20122012-10-15
> > Those DC generators needed not only the reverse-current cutout, but also > > voltage and current regulators. The three relays in the box performed > > one function each. An alternator needs at most a voltage regulator, and > > can get by without even that. How come? > >My motocycle's alternator would run in saturation. The main current draw was for the lights which were always on. Clay
Reply by ●October 15, 20122012-10-15
On 10/15/2012 12:42 PM, clay@claysturner.com wrote:
>> Those DC generators needed not only the reverse-current cutout, but
>> also voltage and current regulators. The three relays in the box
>> performed one function each. An alternator needs at most a voltage
>> regulator, and can get by without even that. How come?
>>
>>
> My motocycle's alternator would run in saturation. The main current
> draw was for the lights which were always on.
>
> Clay
An alternator with fixed field excitation has an equivalent circuit that
consists of an inductor in series with an AC source whose voltage and
frequency are both proportional to rpm. (The magnetic field due to the
armature current directly opposes the excitation field. the equivalent
circuit follows from that.) The result is that the current is constant
when the alternator looks into a short circuit, and nearly so at high
loads, such as your headlights or a storage battery. The diodes, of
course, prevent reverse current. I used to isolate the alternator and
fiddle the voltage regulator to run 110-volt power tools. With no
battery and no voltage regulator, the headlights would blow. As long as
a battery was in place, it set the system voltage.
Jerry
--
"The rights of the best of men are secured only as the
rights of the vilest and most abhorrent are protected."
- Chief Justice Charles Evans Hughes, 1927
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Reply by ●October 15, 20122012-10-15
Jerry Avins <jya@ieee.org> wrote: (snip)> The disconnect relay that you cite is called a reverse-current cutout. I > don't know why it could be expected to fuse, but as I wrote, it can make > a big loud spark. It has both a voltage coil in shunt with the generator > and a current coil in series with it. The way it works, the voltage on > the disconnected generator builds up enough to pull the relay in on the > voltage coil alone. When it pulls in, current flows to the battery > through the current coil, increasing the field that's pulling the relay > in. When the generator slows enough for the current to reverse, the > series and shunt fields buck instead of adding, and the relay drops out.According to the "everything is on the web" rule: http://www.gus-stories.org/november_1968.htm> So why did the Karmann-Ghia generator work after I pulsed the cutout by > hand? Hint: think residual field.For it to work in the first place, the genertor has to supply some voltage with no field current. There is enough "permanent magnet" magnetization in the generator to do that. The first time you power it up the other way, it will reverse that field.> Those DC generators needed not only the reverse-current cutout, > but also voltage and current regulators. The three relays in > the box performed one function each. An alternator needs at > most a voltage regulator, and can get by without even that.> How come?The battery will keep the voltage pretty constant, until it dries up. Excess current electrolizes more water, making more hydrogen and oxygen, and less water. The chemistry of older batteries wasn't so good, and it was normal to add water every so often. Now, many are sealed with no water caps. -- glen
