Andy's Blog

And I mean really used.  This is a tighwad tip for the experts.  Wanna be tightwads need not apply.

It's been a while but you might remember the story of our van.  Here it is in case you forgot:  http://forums.klipsch.com/blogs/andyw/archive/2007/09/21/used-cars.aspx  Now it has close to 160,000 miles.  From the sound of it she needs a new set of coil-on-plug wires and a couple new suspension bushings, but I'm still in love with the cargo room.

But this time my wife's patience has truly been tried.  She is the ultimate trooper.  It takes a special woman to marry an engineer.  But to endure this new level of tightwadedness required an undeniably unique woman indeed...

My youngest turned 4 this year, and my wife after an intolerable hiatus has returned to college.  The "van" was deemed an inappopriate college commuter by my wife.  Now I trust her opinion 100%, but I ran the numbers anyway -- it's what I do.  Calculating the potential savings in gas over the remaining semesters at college, a budget of $2000 was an approximate "break even" point.

Well, I blew that out of the water!  How about $250?

My wife probably had to take a few deep breaths.  And maybe she screamed into her pillow while I wasn't looking, but there it was -- a 1999 Chevy Cavalier, teal green, 4 doors, automatic, good AC, 155,000 miles, and I know the previous owners.  So what that the gas gauge doesn't work, the fan only works on high, and the engine is blown.  Yes, blown.

So $400 later for a junkyard recycled engine, some tune up parts and an oil change, and $150 for a complete interior detail, ozone treatment included, and my wife has a great running $800 commuter... about what you might pay for a set of tires for a BMW.  Speaking of tires it'll need two new ones before the snow flies.  And my wife will tell you that I have to include the price of baby sitting she swapped for my brother in law to install the engine... he went on a Caribbean cruise with my sister.

I've been on vacation with my sister, so I know I got the better end of that deal.

How Low Can You Go?

After stalling and sputtering, winter has hit Indiana this week with a vengance.  Thought it's not yet freeze-yer-eyelids cold, single digit morning temperatures and sub-zero wind chill has furnaces working overtime.

Per HowStuffWorks.com ever degree you turn down your thermostat will save 1-3% on your heating bill.

My home has an electric heat pump. http://home.howstuffworks.com/home-improvement/heating-and-cooling/heat-pump.htm

When the outside temperatures get below about 20-25 degrees Farenheit however, the heat pump can't keep up and we have an "auxiliary" heating unit on the system.  The trouble is that it is a resistance heater and costs a lot more to run.  So when my wife saw that the "AUX" indicator come on this weekend, she started dialing down the thermostat to make it turn off. 

We spent the weekend at a balmy 57 degrees and put on another layer of clothing.  Today the temperature is set at 60.  So if the web site is correct I could save $24-$72 on my heating bill this month, compared to 72 degrees.

 

... And before you ask, she sets the thermostat to 78 in the summer time.

 

Since we are dealing with reactive components we can no longer expect the voltage and current to be in phase.  Last time we left off asking, “What is the phase of the current through this circuit, and how do we get the voltages for each circuit component to add up to 1 Volt rms (the source voltage)?” and we were looking at these graph of the impedance, current and voltage:

 

To calculate the current and voltages requires a bit of math using complex numbers.  Don’t get intimidated by “complex” numbers; solving complex number problems works just like algebra in most cases.  Just remember this: “i” (or “j” as engineers call it) is just a way to account for the “phase” or “rotation” of something.
When we multiply a number by -1, we say it’s the opposite of what it was before.  If it was up, now it’s down, if it was left, now it’s right, if it was a dirt pile, now it’s a hole in the ground.  (Sometimes I wish I were a math teacher).

Now stay with me for a minute… If I gave you directions to Klipsch and said, “Go east five miles” I could also logically say, “Go west negative five miles,” or “Go five miles in the direction opposite of west.”  That is the concept behind multiplying by -1.

Now imagine that to get to Klipsch I say, “Go 3 miles east, turn left, then go 4 miles north.”  If you were a bird and didn’t have to follow the roads, I could say, “Face east, turn 53.13° to the left and go five miles” and you would end up in the same place; (53.13°=arctan(4/3) and 5=√(3²+4²).

When we multiply something by “i” we rotate it 90° counter-clockwise (with polar coordinates zero degrees points to the right and 90°is straight up).  We could also say “turn left”.  If we multiply by “i” a second time, we rotate it another 90°, for a total rotation of 180°, and so on.  If we divide by “i” it’s the same as rotating something by 90° clockwise, or -90°, or we could say “turn right.”

Now it gets fun…  If we rotate something by 90° twice (or A*i²), it’s pointed the opposite direction from where it started, just like when we multiply something by -1 (A*-1 = -A ).  Guess what? i² = -1 so A*i² = -A.  Fascinating!  If we multiply by -1 twice (-1*-1=1) it’s pointing back the way it started.  If we multiply by “i” four times (i⁴) it turns a complete 360° and again it’s pointed the same direction it started.

Complex numbers add, subtract, multiply and divide just as you did in algebra except the “x” is a “j”.
Anyway, back to the point of this blog… To get the phase response we must now concern ourselves with the complex impedance of the circuit components (i.e. their reactive nature), not just the magnitude of their impedance.  Since we left off with 1kHz, we’ll pick back up there:

Z(L)=0+j(2πfL); at 1kHz Z(L)=0+j62.83
Z(C)=0-j/(2πfC); at 1kHz Z(C)=0-j15.92
Z(R)=R+j0; at 1kHz Z(R)=10
Ztotal=R+j(2πfL)-j/(2πfC)=10+j62.83-j15.92; so at 1kHz Ztotal=10+j46.91

Knowing the complex impedance and we can calculate the current.  We will almost always reference the phase of the source, and its phase will be zero degrees, in other words no rotation or phase shift, and the “j” term will be zero, or V=1+j0.

From Ohm’s Law we know that V=I*Z, but since we want current I=V/Z so the current at 1kHz is:

I=(1+j0)/(10+j46.91)

To solve the above expression we multiply top and bottom by the conjugate, or in this case the complex conjugate of the denominator, which is just a fancy way of saying its “reflection” on the “x” or “real” axis.  The conjugate of 10+j46.91 is 10-j46.91 (see picture here http://en.wikipedia.org/wiki/Complex_plane).

I’ll take my time here so you can follow each step:

I=(1+j0)/(10+j46.91)
I=[(1+j0)(10-j46.91)]/[(10+j46.91)(10-j46.91)]
I=[(10+j0-j46.91- j²0)/[100+j469.1-j469.1-j²*46.91²]
I=(10-j46.91)/(100-j²*46.912)
I=(10-j46.91)/[100-(-1)*(2200.5481)]
I=(10-j46.91)/(100+2200.5481)
I=(10-j46.91)/2300.5481
I=(10/2300.5481)-j(46.91/2300.5481)
I=0.00435-j0.0204

Intuitively we don’t really know what this means yet, but let’s take a look and see what we can see.  The current seems rather small, somewhere around 20mA, and since the “-j” term is present we expect a clockwise or negative rotation (i.e. phase shift), meaning the current is lagging behind the voltage. Also since the coefficient of the ”-j” term is about 5 times the real coefficient the angle will be much closer to -90° than zero.

The magnitude of the current using the Pythgorean is:

|I|=√[0.00435²+(-0.0204)²] = 0.02086
|I| = 20.86mA

Now the phase:

Phase = arctan(complex coefficient/real coefficient)
Phase = arctan(-0.0204/0.00435)
Phase = -77.96°

“Holy Cow, Andy!  Isn’t there an easier way?”

Well if you have a cool scientific calculator (or an Excel spreadsheet) that does complex numbers, no!  You just plug in (1,0) divide it by (10,46.91), then hit the button that converts it to polar form to get magnitude and phase.  Man, I miss my HP 28S!  :-(

If your scientific calculator is not so cool then, yes!  There is an easier way.  We start where we started before, but before we do anything we convert to polar coordinates, which is represented by the form (r,θ)

I=(1+j0)/(10+j46.91)

We recognize that j0 means no rotation or zero degrees, so the numerator becomes:

(1,0°)

The denominator requires the Pythagorean to find the magnitude and an arctan to find the angle.

Magnitude = √(10²+46.91²) = √2300.5481  (Now where have I seen that number before?)
Magnitude = 47.964 Ohms
Angle = arctan(46.91/10) = 77.97°  (Hmmmm…)

So altogether the denominator is:

(47.964,77.97°)

And

I = (1,0°)/(47.964,77.97°)

Now we just divide 1 by 47.964 and subtract 77.97 from zero… drum roll….

I = (0.02085,-77.97°)

Or 20.85mA with a phase of -77.97 degrees.

Now we’ll use the computer to do the same thing for the rest of the frequencies.  Here’s the graph:

Now go back to the impedance graph at the top.  When the total impedance is close to the capacitive impedance (we say the capacitor “dominates”) the phase will be close to +90°.  When the total impedance is dominated by the inductor the phase will be close to -90°.  At resonance (the frequency where the capacitive and inductive impedance are equal but opposite in phase) the phase is zero and the load as seen by the voltage source is purely resistive.
Resonance is the place on the impedance curve with the sharp dip, and it corresponds to the peak in the current and voltage curves.  At resonance the complex impedance of the inductor and capacitor are complex conjugates. (i.e. 0+jX and 0-jX).

In this circuit resonance occurs at 503.3Hz.

Well that was a pretty big chunk, so tune in next time and we’ll talk a bit about resonance and find out where all the “extra” voltage comes from!

 

In today’s blog we will use the same values as last time , R=10Ω, C=10μF, L=10mH, and as promised we’ll look at the current and voltage in this circuit:
 
In part 2, we looked at the impedance (magnitude only) of the circuit components, and saw this graph:

 

From Ohm’s Law, V=I*Z, we would expect to see the current as a mirror image of the total impedance, since current is inversely proportional to impedance, or I=V/Z.  So without further adieu:

 
Shown is the magnitude of the current.  The voltage on the resistor, V=I*R, is simply the current times 10, and tracks the current (voltage is directly proportional to current).  If the resistor were the load in this circuit (or a loudspeaker) this voltage curve is the “voltage transfer” of the circuit.  If this were a loudspeaker (assuming it were perfectly resistive, which it never is) and we convert the voltage to dBV, we can just add it to the measured frequency response of the driver to get the frequency response with the filter in place.

For simplicity I always do my calculations by assuming a voltage source of 1Vrms.  This allows me to quickly calculate the effect of the filter in dBV (or dB’s compared to 1 Volt).  For example 0.1Vrms is -20dBV.  In other words if I put 1V into a circuit and get 0.1V on the output I have 20dB of attenuation.  If I look at the 0.1000V line on the graph I can easily see where the response will be -20dB.

What about the phase?  In my effort to keep these things in bite size chunks, both for me and you, this sounds like a good topic for next time.  But I promised to talk about voltages, so before I go, here’s a fun little cliffhanger that’ll stick in your craw…

In a series circuit, the total voltage dropped across the various circuit elements must be equal to the total source voltage.  The source voltage is 1 Volt rms.  The current through the circuit at 1kHz is 20.86mA (you can see it for yourself on the graph above).  At 1kHz the voltage on the resistor is 20.86mA*10 Ohms or 208.6mV.  What about the capacitor and inductor?  (The voltages on the capacitor and inductor are 331.8mV and 1.310V respectively, see graph below.)  So how do you get all the voltages to add up to 1 Volt.  Hint:  What happens at ~500Hz when there is 1 Volt across the resistor?

Now with pictures!

I have been neglecting my blog as of late, so I decided to write at home, and take smaller chunks.  Hopefully the pictures will help to visualize the concepts – it always helps me, I’m a visual type.

In the previous installment we talked about inductors and capacitors, their reactive nature, and how to calculate their impedances.  Next time we’ll talk about the voltage and current and show how the impedances affect the current that flows through a circuit.  After all it’s the current through the voice coil that determines the output level of a speaker.

To start our conversation today we will use a simple series RLC circuit.

The total impedance seen by the voltage source is Z=Z(R)+Z(C)+Z(L).

I’ve picked values for the R, C, and L that will do something interesting in the area of interest – the audio band:  R=10Ω, C=10μF, L=10mH.  So let’s get started by doing an example at 1,000 Hz.

The impedance of a resistor is constant with frequency (at least we are going to assume it is for the time being) so Z(R1k)=10Ω.

The impedance of the capacitor is Z(C1k)=1/(2πfC)=1/(2*3.14159*1000*0.000010)=15.92Ω

The impedance of the inductor is Z(L1k)=2πfL=2*3.14159*1000*0.010=62.83Ω

We could repeat this calculation ad nauseum for every frequency, but since I have a computer…

I went ahead and used a logarithmic scale for frequency since it impossible to see much of anything on a linear frequency scale.  The graph above shows the capacitive and inductive impedance for 10μF and 10mH in the audio band (plus an octave on either end).  Whenever we see a curve in the graph it’s always interesting to see what would happen if we plotted the curve on a logarithmic scale.

And as expected we get straight lines.  Since decibels are logarithmic we can deduce that a capacitor or inductor in the signal path will induce a linear-in- dB change in the current flowing through the circuit.  But that’s a blog for another day.  Just for fun, I added a curve showing the total impedance of the circuit as seen from the voltage source.

One more thing for today… Notice that the impedance of the capacitor falls exactly tenfold for every tenfold increase in frequency, and vice versa for the inductor.  If all you had was a piece of log-log graph paper and knowledge of only one data point, you could draw the entire curve for any value of capacitor or inductor.

Resistance is futile.

As mentioned in Amy's blog, the marketing department served up some some adult beverages during an icebreaker.

This is all part of the Master Plan.

Being a teetotaler, I squeezed a lime into a cup and added ice and water; no sugar for me, thanks.

Evidence of the progress of the assimilation was had yesterday in the Klipsch Cafe.  Amy has been sitting at the "engineer's table" for a long time, so that doesn't count. (The "engineer's table" is the rough equivalent of the geek/nerd table in the high school cafeteria.)  But yesterday Matt and Phil joined us at our table... now granted, they could probably be considered the "A/V Club" and the "popular/cheerleader/jock" crowd probably can't tell the difference.

Phase II has begun.

Don Inmon and Phil Hatch will sometimes venture onto our turf too.  Mike Klipsch and Paul Jacobs aren't strangers either.

Jill and Meredith will be the ulimate test of the assimilation, but once they see all their friends hanging out with the geeks, what choice will they have?

 

Inspired by a conversation at the lunch table...

11. Excetera (et cetera) - Eleven because, well, at Klipsch we just think it ought to go to eleven.

10. Libel (liable) - Yes, I know, libel is a word, but that's not what you mean.

9.  Nucular (nuclear) - I think we're all tired of this one.

8.  Wheelbarrel (wheelbarrow) - OK, you get a pass on this one; it makes sense, but I still get a kick out of it every time my wife says it.

7.  Upmost (utmost) - I reckon that half the country has never heard this word pronounced correctly.

6.  Expecially (especially) - Favorite of English teachers everywhere.

5.  Sherbert (sherbet) - Don't feel bad, hardly anyone says it right.

4.  Dialate (dilate) - What the ophthalmologist (<--- didn't make my list, but is both commonly mispronounced AND misspelled) does to your pupils.

3.  Acrossed (across) - No matter how hard you try, you'll never get your point "acrossed."

2.  Realator (realtor) - Two syllables.

1.  Irregardless (regardless) - Regardless gets jumbled with its synonym, irrespective.

And one to fight over...

Comparable - KOM-per-a-ble, not kum-PARE-a-ble

 

Holiday Shopping

Set a budget. Stick to the budget. Do not use credit.

Know what the people for whom you are shopping want.  If you don't know what they want, ask them.  Ask them what stores they actually shop at, so the gift card won't go unused or unappreciated. We have friends who bought a fixer-upper and do lots of home repairs.  They get a Lowe's gift card every year.  Everyone else gives them a Lowe's gift card too.  They are able to make significant purchases when the items they need go on sale.  They actually appreciate the gift cards; they don't consider it a cop out gift at all.

Make a list. Trim the list. Shop from the list. Do not impulse buy. Do not use credit.

Pay cash, or use a debit card. Do not use credit.

Keep the store receipt. Forget about gift receipts, They force people who hate your gift into getting "store credit".  If they return it, they're going to know how much you spent anyway.  Pay cash (don't use a credit card), otherwise they might want to refund your card instead of the recipient being able to get cash they can spend somewhere else.

For the person who has everything; don't waste your money on more stuff. What restaurant do they like? (gift card) Movie theater close by? (gift card), Opera? Symphony? Museum? Sports fan? (tickets) Always buy two, or put enough on the gift card for two.  Going out to eat by yourself is lame. Ditto for the symphony.

And for the guy who has five kids, offer to babysit so that he can take his frazzled wife to the mongolian barbecue and a movie.

Save your gift boxes, bags, bows and tissue paper to use next year. If this causes them to think your cheap then tell them you'd gladly reduce the amount of their gift by $5 so you can stick it in a useless bag (sorry, is my "guyness" showing through?).  Or if you want to go high-class, tell them your doing it for the planet.  Heck, I've been re-using some of my boxes for as long as six or ten years. Eventually though, I will run into another tightwad who keeps one of the boxes that I put his gift in. These guys get wrapping paper the following year.

Do not use credit.

And remember to put something on your list for the less fortunate.

 

"...and secure the Blessings of Liberty to ourselves and our Posterity..."

My great-grandfather, James, was in the Ohio infantry during the Civil War. My great uncle, Donald, died in Bologna, Italy in 1944.  My father, George, served in 1961-1962 in the 3rd Armored Cavalry in West Berlin, Germany, guarding the autobahn.  I have several other cousins and uncles who served.  I'm sure all of us know someone who served. 

Most people know the first verse of our national anthem: 

Oh, say can you see by the dawn's early light
What so proudly we hailed at the twilight's last gleaming?
Whose broad stripes and bright stars thru the perilous fight,
O'er the ramparts we watched were so gallantly streaming?
And the rocket's red glare, the bombs bursting in air,
Gave proof through the night that our flag was still there.
Oh, say does that star-spangled banner yet wave
O'er the land of the free and the home of the brave?

But many have never heard the fourth, sung in more formal occasions:

Oh! thus be it ever, when freemen shall stand
Between their loved home and the war's desolation!
Blest with victory and peace, may the heav'n rescued land
Praise the Power that hath made and preserved us a nation.
Then conquer we must, when our cause it is just,
And this be our motto: "In God is our trust."
And the star-spangled banner in triumph shall wave
O'er the land of the free and the home of the brave!

 

Peanut Butter Jars

My father was a packrat extraordinaire, so I learned from the best.  He had dozens and dozens of peanut butter an mayonnaise jars on shelves he built for them that line the garage wall.  The shelves are very sturdy, and not a one has sagged in 25 years.  The jars were used as containers for everything from screws to nuts.  The clear glass made it easy to find what you are after, but if you get in too much of a hurry you'd be sweeping up glass shards from every corner of the garage.  It was priceless the first few times my new brother in law would ask if I had a certain something for some project he was working on.  The answer was always, "Yes, take a look in mom's garage.  I know dad kept a jar of those somewhere."

As I struck out on my own, and having the memories of sweeping up the inevitable glass on the floor, I thought I would be smart and bought a few of those neat little plastic drawer sets for all the little odds and ends that get collected.

Then an amazing thing happened... they started making peanut butter jars out of plastic.  My neat little drawers are now an afterthought - one still has the plastic wrapping on it.  I now collect all my peanut butter jars.  I have recently also found a use for mayonnaise jars in one of my hobbies, so I'm collecting those too.

Peanut butter jars blow the drawers away in usefullness, they don't shatter on contact with the garage floor, and they are much much lighter than glass.  They also have the added advantage of being portable.  Drawers of screws and nails get dumped if you have to take them somewhere for project.

Cleaning them is easy.  Fill halfway with hot water and little dish soap.  Shake and let stand.  Every time you walk by for a couple days, give the jar a shake, then wash normally with the other dishes.  To get the label off, soak it in the rinse water after the other dishes have been washed.

 

Every analog signal when reduced to its most basic form will be a sum of sines. Even a square wave is the sum of a series of the odd harmonics (integer multiples) of the fundamental.

It is the harmonics that give different instruments their unique sounds. Change the harmonics and you change the sound. Take the trumpet and the clarinet. Both reproduce essentially the same range of musical notes on a scale, but hardly anyone could mistake one for the other. There are other non-harmonic cues as well, but absent these, the distinction is still very clear. Sending all these frequencies to the correct drivers (woofers, mids, and tweeters) in the correct proportions ensures that the resulting sound is a faithful reproduction of the original.

Filter design is necessary for every Klipsch system, and every analog filter, whether passive or active, is made up of a few basic components: resistors, capacitors, and inductors (active filters add a transistor or op amp)

Each of these components has its own particular relationship with voltage (V) and current (I), described by the following equations:

V = I*R where R is the value of the resistor.

I = C(dV/dt) where C is the value of the capacitor.

V = L(dI/dt) where L is the value of the inductor.

Engineering textbook convention says that when you see capital “V” and “I”, they describe DC voltages and current, and when you see lower case “v” and “i” (usually in a script font), they describe AC voltages and currents. I will ignore that for the most part here to make it easier to read. (Likewise the “d” is usually a greek "δ" and “t” is sometimes printed in a script font).

Capacitors and inductors are reactive components. In a nutshell they store in energy in an electric or magnetic field, respectively. From the above equations you infer that you can not change the voltage across a capacitor instantaneously, nor can you change the current through an inductor instantaneously (in other words, no step functions), and when AC voltage signals are applied, there is a relative phase difference between the voltage and current through these components. In a capacitor, the current leads the voltage by 90 degrees, and in an inductor the current lags the voltage by 90 degrees.

The unit of measure of capacitance is the Farad, and is a rather large quantity. Most of the time we deal with microfarads (10^-6 Farads) and picofarads (10^-12 Farads). The unit of measure of inductance is the Henry, and mostly we deal with millihenries (10^-3 Henries) and microhenries (10^-6 Henries).

“Impedance,” which is frequency dependant, is the term we use in place of “resistance” when we’re dealing with AC signals and reactive components, and is denoted by the letter “Z”. “Reactance” is used to describe the impedance of capacitors and inductors and is the purely imaginary component of impedance, and is denoted by the letter “X”.

What is imaginary? In mathematics, the square roots of negative numbers are described as imaginary numbers, and the term “i” is given to be the value √-1. In engineering we use the term “j” instead (“i” was already taken, see above).

When you combine the real (resistive) components with the imaginary (reactive) components, you end up with complex numbers to describe the impedance.

Ideal capacitors and inductors do not dissipate any power, they store all the energy, and will give it back to the circuit whenever allowed to do so. Real world components always have “parasitic” components, so they are not purely reactive, and we have to take that into consideration in the design, especially any resistive parasitics, since this directly affects the magnitude of the signal going to the loudspeaker.

The reactance of capacitors and inductors is given by the following:

X_C = -j/ωC or 1/jωC (where ω is angular velocity in radians per second)

X_L = jωL

Impedances work just like resistances when using Ohm’s Law, but you end up doing math on the complex numbers to obtain the result.

So, a couple quick examples are in order. What is the reactance of a 1uF capacitor and a 1mH inductor at 1kHz? (Remember, ω=2πf where f is frequency.)

X_C = -j/ωC = -j/(2*π*1000*0.000001) = -j/0.006283 = -j159.2 or -159.2j

X_L = jωL = j*2*π*1000*0.001 = j6.283 or 6.283j, whichever you prefer.

Notice in both examples the “real” part of the overall impedance is zero, i.e. 0-j159.2 and 0+j6.283.

Now for a little fun with the previous two components, and a 1kΩ resistor in a series circuit.

For a series circuit Z_TOTAL = Z₁ +Z₂ + Z₃ + … + Z_N So,

Z_TOTAL = Z_R + Z_C +Z_L = (1000 + j0) + (0-j159.2) + (0+j6.283) = 1000-j152.9

Notice that at this frequency, the reactive part is overall capacitive (we know this from the “-j” term), meaning the current through this series circuit will lead the voltage somewhat. How much? We’ll have to find the phase angle, but since 152.9 is “small” compared to 1000, we expect to see a small phase angle.

A really cool trick for finding the phase angle can be done geometrically, using what is called a “phasor diagram”. Simply put a phasor diagram is a graphical representation using vector summing of the real and imaginary parts of the result, and will give us both the magnitude of the impedance, |Z|, and the “direction” or phase, φ, of the current. On the “x-axis” we put the real part of the term, and on the “y-axis” we put the reactive (imaginary) part of the term. See http://en.wikipedia.org/wiki/Complex_plane

The phase angle of the current then is, φ = tan^-1(152.9/1000) = 8.7°

And the magnitude of the impedance is found using the Pythagorean Theorem, a² + b² = c², and

|Z| = √[1000² + (152.9)²] = 1012.6 Ohms.

At 100Hz the impedance is Z = (1000+j0) + (0-j1592) + (0+j0.6283) = 1000-j1591, having much more influence from the rising impedance of the capacitor at low frequency. The magnitude of the impedance has also changed, increasing to 1879 Ohms, with a corresponding reduction of current flow.

At 10kHz the impedance is Z = (1000+j0) + (0-j1.592) + (0+j628.3) = 1000+j680.7 with more influence coming from the rising impedance of the inductor at high frequency. The magnitude of the impedance at this frequency is 1209 Ohms.

The phase angle at 100Hz is 57.8°, while at 10kHz the phase angle is -34.2° and the current lags the voltage.

In a series RLC circuit there always exists an impedance minimum. This occurs when the magnitude of the inductive and capacitive reactance are equal (graphically they will cancel out on a phasor diagram and the contribution to the magnitude of the LC part of the circuit is zero Ohms). This occurs at the frequency ω = 1/√(LC), and is called the resonant frequency.

In our example, this happens at f = 1/[2*π*√(0.001*0.000001)] = 5033Hz. At this frequency the magnitude of the impedance is 1000 Ohms and the phase angle of the current is zero, φ = tan^-1(0/1000) = 0°.

Knowing what you know now and applying Ohm’s Law you can pretty much describe any RLC circuit in various series and parallel combinations at any given frequency. Powerful stuff. Yes, it can get quite tedious with several circuit components, especially when you throw the driver model into mix. But that’s why we invented computers.

All for now, when I get time to get back to it we’ll look at some simple passive filters.

I'm a sucker for a well though out, well executed design.  My brother-in-law and I are both engineers, and we like talking about good and bad designs.  Usually we lean toward criticizing the bad ones.  Apparently other people do too, as there are web sites devoted to it.  I don't have a web site, but I have a blog, so here's my first good design/bad design blog.

Topic: ice cubes

Good Design:  I love the Arby's "duck turd" ice. [(c)AHW 2008, all rights reserved]  An informal poll at the lunch table revealed that others too love the duck turd ice.  If you don't know what I mean you'll just have to get some yourself and see what I mean.  The ice gets your drink real cold real fast, and as a bonus it's easily crunchable (I like to eat ice, I know, it's bad for my teeth, yadda, yadda...)

Bad Design:  The ice that comes out of about every home ice maker.  Who designed these things?  Did they ever actually try to use the ice that comes out of them?  The shape of the ice is a round bottom with a flat top, kind of like a crescent moon shape.

The problem with this ice, and I'm sure you'll all agree, is that the radius of the bottom curve of the ice closely matches the inside radius of common beverage containers (cups, mugs, glasses, tumblers, etc.).  When a beverage is consumed the ice invariably turns itself perpendicular to the flow of the beverage.  Thus the ice creates a small dam of sorts to the intended imbibing of the desired refreshment.  If he cares to drink more than a trickle, this requires that the intended recipient of said liquid refreshment tilt the glass ever higher in an attempt to obtain the optimal flow.

The attempt to obtain an adequate swig then results in the ice dam being overtopped, with an overabundance of beverage gushing uncontrollably toward the intended recipient's face, along with the unintentional social embarrasment and the attendant quips and comments about having a "drinking problem."

No, this isn't a blog about a BMW, although my brother-in-law used to own a 535i 5-speed, and I thoroughly enjoyed driving it.  This blog is about the "Klipsch: The Ultimate Sound Experience" license plate and the 1999 Jeep Cherokee attached to it.

Klipsch more than likely ripped off the tag line from BMW, not a stretch considering several people at Klipsch drive them.

Some years ago, all the employees got said license plates, and I proudly attached mine to the front bumper of my Jeep.  Since the Jeep is also black it matched perfectly.  Also if you look closely at my avitar you can see that I am a member of JP Frog Offroaders, www.jpfrog.org, dedicated to the mangling of sheetmetal and the snapping of axle shafts.  My aspirations don't quite extend that far, but a few months ago, after the loan was paid and after a few years of neglect, the Cherokee got a much needed supension lift, tow hooks, and 31" tires.  Not large by any means, but adequate for semi-serious excursions off the beaten path.  The "normal" Jeep in my club rides on 35"-37" tires, and about half of them have axles swapped in from full-size trucks.  A couple more own Wranlger Rubicons which come from the factory with Dana 44 axles, locking differentials (I'll get to that later) and a 4:1 transfer case.  A week ago we went to the Wilstem Ranch between Paoli and Frenck Lick, Indiana.  One guy even brought out his brand new 4-door Rubicon, with only 1,000 miles on the ticker.

Needless to say, while most of the rest of the group were climbing of two-and-a-half foot rock ledges, I was taking the bypass.

I took the girls along for the 'wheeling/camping trip, partly because I had taken the boys out earlier this year, a partly because of the tightwad factor (children under six are free, and Allison is 4).

A few times I had to make a second or third run up the trail to get through or unstuck, but my Jeep was no match for one partiular ravine.  It had a couple large flat rocks, which when wet were a slick as ice.  When I tried to drive across, I slid sideways further down the ravine.  At the low end my right rear tire slid into hole filled with loose rock and sand.  On the other corner, the tire was lifted about six inches off the ground, and hence no power at the front axle.  Without any traction at either corner, forward and reverse travel came to a halt.  After a few tries it was ovious that I would only succeed in digging a deeper hole under the right rear and out came the winch cable.

A "locker" http://en.wikipedia.org/wiki/Locking_differential would have made the difference, since I still had adequate traction at the other two wheels.  'Wheeling the Cherokee is an interim step, as I'm in the middle of a very long build up of a 1984 Jeep CJ-8 http://en.wikipedia.org/wiki/Jeep_CJ#CJ-8.  The current plan is fiberglass body, 4" lift, 33" tires, front and rear lockers, 4.10:1 axle ratio, and a Ford truck T-18 transmission http://www.novak-adapt.com/knowledge/t18_t19.htm, which I have already rebuilt and adapted to the Jeep transfer case.

The Cherokee performed admirably, as well as the Scrambler in stock configuration on 31"s.  Here are a few pictures of my "stuck." (Note the Klipsch license plate.)

I have always had pet peeve when travelling with the family, albeit a lighthearted one... it would save so much time if my wife's bladder were as big as the gas tank.  But it's not just her, there are children involved too.

Some years ago we took a trip to Marco Island, Florida.  We had a wonderful time.  My wife had a thing, so she couldn't enjoy the long road trip with me and the boys, so she flew down the next day, holding the baby girl on her lap.

Travelling with the boys was a joy.  We would pee, eat, and fill up the tank, then drive five hours, stop, pee, eat, and fill up the tank.  Lather, rinse, repeat.  If it weren't for the two hour traffic jam near the Georgia border we would have made it halfway through Florida before stopping for the night.

On the way home we didn't even make it out of Georgia before the girls had had enough, and we stopped for the night.

But now, even my bladder has been bested.  You may remember that last year I bought a big Ford E-150 van.  It replaced a Mazda MPV that got an "OK" 17mpg on the highway with the AC running.  Well, yesterday we drove from Indianapolis to Lansing, Michigan and back for my family reunion.

I filled up at the local Marathon station and headed out.  Last night I pulled into the same gas station, pulled up to the same pump, and once again filled the tank.

Here are the stats:

500.9 miles, 30.149 gallons, 70 mph with the AC on low, two gas stops (for the vehicles following us), one stop for Subway, and three rest area stops (including one for me).

I have a 35 gallon tank, so I could have gone another 80 miles.  My wife gave me a dirty look for suggesting it though, as the gas needle was pointing straight at the red line.

The fraction gurus out there will see 5/3 and deduce that we got 16.6 miles to the gallon.  Impressive for a big brick with a 5.4L V8.

Use it Up, Wear it Out, Make Do, or Do Without

An old mantra that could use a little dusting off. I was reminded of this tidbit after a conversation with a coworker today. I sometimes think about how different life was for our parents and grandparents. Money didn't grow on trees. Nowadays you can finance dinner and a movie for 30 years at 14.99%.

When my granparents moved into the nursing home their old wringer washer was still being used. I have no idea how old it was, but it was older than their house. These days our expectations of quality and reliability when it comes to certain consumer goods have really taken a nose dive. My mother still uses the pans she was given as a wedding gift. That was 49 years ago. I've been married almost 12 years and I'm on my third set.

Of course there are examples good quality... my 60GB Western Digital hard drive comes to mind. As of yesterday, it's now attached (by a USB cable) to it's third computer. Apparently people get miffed when their hard drive dies.

In less that a year, through no fault of its own, my TV will go dark... well OK, it'll go staticky. I've been married 12 years and I have yet to pay for a TV. (Yes my tightwadedness goes way back!) The current one is so old/cheap that it doesn't have even a composite video input. Just a F-connector for the antenna. To watch DVDs I had to get a modulator. It didn't have a remote when a friend of mine got rid of it, but I discovered that my VCR remote (same brand) would perform the major functions. The remote doesn't work anymore... or the kids lost it, I don't know which... but when you have 5 children there's always someone around to change the channel.

I don't know of anyone getting rid of a flat panel TV with a digital tuner, so when the last analog TV transmitter is turned off I will probably just do without for a time.