[Audiovista]

A simple theory behind square wave

In order to better understand what exactly happens when the cartridge load changes, it will be useful to  learn more about square wave - a standard way of quickly getting a big picture of any  signal amplifier behavior.

An ideal square wave is a periodic waveform that has only two distinct levels, with infinitely fast transition between them.



What makes the square wave interesting is that it can be represented as an infinite sum of sinusoidal waves. Frequency of the sinusoidal waves is multiple of the fundamental frequency of the square wave, and each sinusoidal wave is called "harmonic". The first harmonic, which is also called a "fundamental" is a sine wave of the same frequency as the square vawe. The graph below shows square wave and the first harmonic:



The second harmonic is a sine wave with frequency two times higher than the opriginal square wave. Adding it to the first harmonic, the combined waveform starts to resemble the original square wave:



Adding the third harmonic (sine wave of three times higher frequency) further improves fidelity:



A waveform with first four harmonics is illustrated below:



Continuing to infinity, the sum of the harmonics will recreate a perfect square wave.

Wikipedia offers an excellent animation of the above process:
http://upload.wikimedia.org/wikipedia/commons/7/72/Fourier_transform_time_and_frequency_domains_%28small%29.gif

NOTE: Blue lines in Wikipedia animation represent spectrum of the signal - amplitudes of all sinusoidal components that make the original signal.

So here it is: looking at a square wave, we are simultaneously looking at signals of many different frequencies and amplitudes - not unlike typical music signal, only easier to consistently recreate, measure and understand.

Next: we'll take a look at some real life square wave signals and what they tell us. Questions, comment and any other active participation is welcome 

[*Scotty*]

Do you have a source for a test record with 1kHz square wave on it? We could learn a lot about the RIAA equalization and how well the cartridge is set up.
Scotty

[Audiovista]

You are absolutely right - that would be a very useful tool. Unfortunately I was not able to locate such a test record. I am wondering if an electromechanical fixture can be made to simulate the effect - piezoelectric transducer, or similar, that would move the needle left-right.

[*Scotty*]

A Stereo square wave and a dual trace scope would be a good combination.  Perhaps if we lobbied Acoustic Sounds to produce a test record ala the old CBS series of test records? If they would even produce one with a square wave and a low distortion sine wave, we could test a number cartridge parameters. I would like to able to test THD and IM as well as frequency response and separation.
Scotty

[tomytoons]

One of these?

http://www.ebay.com/itm/CBS-LABORATORIES-Frequency-Test-Record-STEREOPHONIC-STR-100-/230760825691

This is one of a series I guess. Not cheap, 1961 date.

http://www.musicstack.com/album/cbs/stereophonic+frequency+test+record

[Audiovista]

Instead of a square wave, series of low distortion sine waves, with very accurate levels, could be used as an alternative, even though the process would be much more involved and little less accurate. But "squares" are hard to beat...

[Audiovista]

Real life examples

A perfect square wave is.... well, perfect. Most of the low signal amplifiers (line, phono preamplifiers, etc.) can come very close to that, especially when signals are low (1 Volt or less). When it comes to higher levels, distortion mechanisms take over and make the square wave look less than perfect, sometimes very much less. Power amplifiers output highest level signals, and distortions are that much easier to notice.

A good Solid State amplifier, at lower frequencies (1kHz) should reproduce square wave quite faithfully. At higher frequencies (10kHz) bandwidth limitations become visible. Still there should be no evidence of overshoot or ringing. An example of a good solid state amplifier at 10kHz is below:



A tube amplifier can be allowed little more distortion, after all that is what makes their sound different. A couple of examples of good Push Pull tube amplifiers at 10kHz are given below:

   

Single Ended amplifiers are quite different beasts. Distortion is much higher  and waveforms are much farther from perfect, but waveforms shown below are still very acceptable (left graph is 1kHz sgnal and the rigt one is 10kHz):

   

Obviously, that should not be acceptable for a Solid State amplifier and should be avoided in a Push Pull tube amp, but it is perfectly fine for even high end Single Ended topology.

Now, some illustrations of what is not acceptable, and should be avoided, no matter how the unit sounds - there is just something very wrong with the design  in the following examples:

This signal shows overshoot and high frequency ringing followed by a subharmonic oscillation:



The signal below has large overshoot and  oscillations that do not stop (sadly both examples belong to one ultra expensive amplifier):



The oscillations below are so bad that there is a likelihood of emissions that will negatively affect other nearby equipment:



For full disclosure, here is how Vista Amplifiers perform with a square wave.

model  i34 (Push Pull tube amplifier) at 1kHz  and 10kHz (model i84 has identical response):

   

And the inexpensive model i82 (Single Ended design), also at 1kHz and 10kHz:

   

Even if an amplifier is as inexpensive as model i82, it still has to perform without oscillations, ringing or overshoot. In fact, there is no price point below which an amplifier should not meet basic criteria of operation without crippling artifacts.

Armed with this knowledge, we can now move to examining loading effects on cartridges.

[fredeb]

Really interesting read , I need to get myself one of those test LP's and a mike .