Introduction

When building my own gainclone I decided to make a 12-step attenuator based on a rotary switch and some resistors just like the original gaincard amp.
Most people (including myself) think that a stepped attenuator gives better sound quality than a quality pot.

1.1 Why use an Attenuator

Why change your pot to a 12- or 24-step attenuator, or build your new amp with an attenuator instead of a potentiometer? Is it worth the trouble to change, and how much will you win?
Well, your mileage may vary, but in general the log pot used in many amplifiers could (over years) suffer from the following problems:
  • Channel tracking might differ from 10% to up to 20%, with descrete resistor values it is possible (especially when measuring and matching before use) to get both channels within 1 a 2% over the full range.
  • Cracking and popping due to wear of the carbon/cermet resistor elements.
  • With dual-mono setup it is nearly impossible to get both channels in the same position (same gain).
I use an ALPS blue pot in my UL40-s2 amp, and I'm very satisfied. However, after the warranty period is over I might try an upgrade with just 12 resistors. Listening to the gainclones I've built with these switches its safe to say that this is a very good way to control your amp. Especially if both channels have their own volume control, it gives a reference for putting both channels in exactly the same position, something that's nearly impossible to do with a regular pot.
There are standard 12-step switches available from your local electronics store, and these are most likely mass production pieces that will do perfectly. However, there are also 24-step pieces available but sold new these are far more expensive. A cheaper alternative is to look for used switches in army-junk shops.
The photo on the right shows the Lorlin switch of just € 1.50 or so with 12 resistors that makes up the 12-step switch for Geenkloon (and Cyclone). The (big) shielded microphone cable connects ground and signal in, the thin silver/PTFE wire outputs the attenuated signal to the amplifier stage.
In the remainder of this page, I will describe the construction for a 12-step switch but the principle if the same for 24-step switches as well, it just requires a little more resistors and soldering.

1.2 What's the problem?

Like most other builders I knew how a 12- or 24-step attenuator should be constructed, but I needed to calculate the right resistor values for each step based on the desired input impedance, the number of steps and the desired maximum attenuation. The input impedance is often specified by the project you're working on, in my case I was working on the Gainclone with an input impedance around 20 kOhms.
The number of steps results from available switches, the amount of money you want to throw at it and your ears. I discovered that I can easily live with a 12-step attenuator, but of-course a 24-step (another standard value) would do much nicer. However, it is very important to define the first steps really well as they determine the critical low volume levels (candle light music etc.) and should be such that the sound level does not disturb conversations etc.
The maximum attenuation in dB will be 60 or better. For a 12-step project make it at least 48dB, but for a 24-step switch you might want to use a value of 60 dB or better.
The most simple way to make a 12-step attenuator with logarithmic volume control is of-course to make sure that every step of the attenuator has the same value in dB (which results by definition in a logarithmic gain). However, I found especially that with 12-step controls it's much better to tune the steps to your own favorite sound levels. In my case I might want the first steps to be fine, a mid section with more coarse steps and the last three steps to have steps that are three times as steep.

2. Designing an Attenuator

In the following sections it is described how to design your own attenuator, and how to do the math for calculating the resistor values etc.

2.1 Architecture

Things to take into account when building your own volume control with a stepped attenuator are :
  • What is the design of the next stage of the amp we're feeding the attenuator output into: Non-Inverted or Inverted?
  • What is the output impedance of the CD-player, tuner or phono amp feeding into the attenuator?
  • What is input impedance we want to create for the input of our amp?
  • How many steps do you need?
  • What are the steps in dB we want for Volume control: linear or a particular curve based on our preferred volume levels?
  • What type of switch do we have: Make-before-break (=shorting) of break-before-make (non Shorting)?
  • Is there a ground resistor from the input pin of the amp to ground (mostly used to give the amp a DC reference point), then we should take this resistor into account as it is a parallel resistor between wiper and ground and influences both impedance and gain (inverted amp).

Basic Principle

There are several ways to build a volume control for an amplifier, although all methods described below are based on a variation of the voltage divider. The basic circuit looks like this:
And the "gain" of a voltage divider is defined by the following formula.
And as we know the formulas for calculating the gain we can also work in the reverse direction and calculate resistor values for a given gain of the attenuator (which will mostly be negative e.g. -60 dB)
These two formulas are the basis of all attenuators described on this page.

Series Attenuator

The series type consists of a chain of resistors connected between signal source and ground forming a constant input impedance. The wiper takes position between any adjacent pair of resistors and forms a classic voltage divider with all resistors from that position to the signal and all resistors from that position to ground. For the series attenuator you need a 12- or 24-step switch with only one deck.
The series attenuator has a big advantage: Only a simple switch with one deck of 12 positions is necessary, and only 12 resistors per channel are used. The simple construction makes it less prone to failure. The disadvantage is that at most positions of the switch there are more than one resistors in the path to the signal source and also more than 1 resistor to ground. At the lowest listening levels there are 10 or 11 resistors in the signal path.

Series attenuator with ground resistor

A common variation of the series attenuator is the attenuator with shunt resistor (signal to ground). The reason for such a shunt resistor is normally to provide a defined impedance to ground to the amp input. Common reasons for presence of such a resistor are:
  • There is an audio capacitor between the line input (with it's attenuator) and the input of the Opamp to protect the amplifier from DC offsets. The resistor provides a DC ground reference for the Opamp input.
  • The attenuator is of the break-before-make type and therefore between switch positions there is a moment where the ground reference is not present. A permanent resistor between the wiper and ground will provide such an impedance at all time.
  • The amp is used as a power-amp only and in order to protect the speakers when disconnecting the pre-amp the resistor provides a reference to ground.
The figure at the right explains the principle: Rg is used to provide an impedance to ground and influences the attenuator (Ra and Rb for a certain position). When designing an attenuator for such environment it is good to remember that the effective input impedance of the amplifier at the signal input terminals will vary over the range of the attenuator.
As a result, care must be taken to select the right values for the resistors in the attenuator so that the impedance of the amplifier as seen by the source (Cdplayer etc) will not deviate too much from the desired values.

Ladder Attenuator

Figure 2 shows the setup of the ladder version. The rotary switch makes two connections at a time, connecting on one side to the signal in and to the other side to ground. The wipers are both connected to the signal out that is fed to the next amplifying stage. For the Ladder type you need a switch with two decks.
The ladder type of attenuator has a big advantage over the series version: Only one resistor is in the signal path and there is always one resistor to ground. The voltage divider always consists of two resistors Ra (to signal input) and Rb (to ground) and the wiper connects the two to the output of the attenuator.
The ladder attenuator therefore in fact contains 12- or 24- voltage regulators, which makes it the most elegant (and expensive) solution for volume control.
Resistor 12b may be omitted and replaced by a short to ground if the volume needs to be really 0 in the lowest position.
I updated the Excel spreadsheet, to include a ladder attenuator for both a 12- and 24-step switch.

Shunt Regulation

The shunt type is a mix of the ladder and the series version and offers in most of its range the advantages of both. The shunt type is not usable in all amplifier designs.
The advantages of the shunt regulator are in principle the same as for the ladder: Only two resistors (except in position 1) are in the signal path. The disadvantage of this design is that the input impedance is not flat but is a value of Ra + Rbx and thus changes with every value of x. For tube pre amps special care must be taken that the input impedance still is high enough for the tube pre amp.
In most cases resistor number 11 will be replaced with a hardware to ground so that there is no signal on the output in the lowest volume position. However, with a 12-step attenuator its a choice to use position 12 for very soft music and not completely shut off the amp.

2.2 Building a 12-Step Series Attenuator

Let's start with a 12-step attenuator for non-inverted designs such as my GeenKloon project. Such attenuator switch is based on the principle of voltage-divider: Eleven, Twelve (or twenty-four) resistors are connected in series, and the rotary switch positions between two resistors. The effective attenuation on pin "pos" of the voltage divider then can be computed as shown in formula 1a below. In this example I assume 11 resistors for a 12-step attenuator which means step 1 is full power and step 12 is 0 volume (wiper connected to ground). But it is equally possible to give step 12 a resistor value to ground which means that the volume then is low but never completely off.
Figure 1a is the schema for the attenuator I used for the GeenKloon (my non inverted version of the gainclone based on a LM3875 chip):
It is very advisable to observe the resistor values and solder them the right way (determine which is pin 1 and which is pin 12) because it's easy to build it the wrong way around which results in poor (hardly no) attenuation at all.
Well, the above formulas allow you to calculate the resulting dB attenuation on every position given that you know all resistor values already. And of-course this is where the problem is, since we would like to work the other way around: First determine the number of steps, the maximum attenuation in dB and the input impedance of the circuit and then calculate the corresponding resistor values.
Because this requires more than just a few calculations I wrote an Excel file that does just this and is easy to use. The following table contains example output from the spreadsheet for some typical impedance values.
Attenuator Attn dB Resistor
10k
20k
50k
100k
Step 1 (lo) -60 R1
10
20
51
100
Step 2 -54 R2
10
20
51
100
Step 3 -48 R3
20
40
100
200
Step 4 -42 R4
40
81
200
390
Step 5 -36 R5
81
160
390
820
Step 6 -30 R6
160
330
820
1,600
Step 7 -24 R7
300
620
1,600
3,000
Step 8 -18 R8
620
1,300
3,000
6,200
Step 9 -12 R9
1,300
2,400
6,200
13,000
Step 10 -8 R10
1,500
3,000
7,500
15,000
Step 11 -4 R11
2,400
4,700
12,000
24,000
Step 12 (hi) 0 R12
3,600
7,500
18,000
36,000


TTL:
10,041
20,171
49,912
100,410

2.3 A series attenuator with ground resistor

As described above in the architecture overview there are amplifier designs where apart from the attenuator there will be another resistor parallel to ground. This resistor is normally connected between the amp input and ground. the capacitor is there to assure that there will be no DC offset voltage at the speaker output.
On the right the principle is found in a figure where I modelled the amplifier with a power opamp (as used in gainclones) and the attenuator with the Ra and Rb resistors in the ellipse. And for the sake of this exercise we assume that the value of the capacitor is such that the lowest frequencies in audio land are passed through this capacitor (for filter background the reader is referred to the RIAA/filter background pages). The ground resistor Rg can also be used to make a non-shorting switch more usable for an amp, in this case the capacitor may or may not be present. If the resistor is not present the resistor will probably be soldered directly on the attenuator between the wiper and ground.
 
These formulas are used in the spreadsheet (found on the download page).

2.4 An Inverted Amplifier Design

For inverted designs we must use different resistors values for the same dB steps as in a non-inverted setup. The reason is as follows:
The gain of an inverted design is determined by the feedback resistor and the effective impedance found on the inverted input of the OpAmp. And here lies the source of the problem; The attenuator is in series with this resistor on the inverted input and therefore part of the gain loop as well. Moreover, the output Z of the source device (CD-player, preamp, phono pre) is also in series and plays a role in the gain calculation, especially when using tubes on the input.
Important is to recognize that the attenuator itself still behaves exactly in either setup, and that the effective attenuation measured between input and ouput of the attenuator is independent from the amp architecture chosen. However, in an inverted setup the total attenuation/amplification of the amp is influenced by the attenuator itself and therefore we deal with it in this chapter.
The following figure illustrates the issue described above. Clearly is shown how the input resistor Ri is in series with the effective impedance of the attenuator and the output impedance of the connected source equipment (CD-player or other preamp). The attenuator is modeled with Ra and Rb: On any given position of the wiper, Ra defines the sum of all resistance to signal and Rb the sum of all resistance to ground (R_a + R_b = constant).
In the schematic, I omitted other components such as the input cap, as these were not necessary for an understanding of the issue. The gain of the OpAmp is therefore determined as follows:
Therefore the calculation method used for non-inverted designs does not work a 100% for non-inverted designs and that calculating the optimum gain requires even more compute power. Well, let's first see what role each component plays in the equations.
In order to make a rotary attenuator switch for inverted mode amplifiers, we need to find the resistor values for any given attenuation step between two switch positions. After all, it's nice to be able to calculate the attenuation for a given resistor setting, but rather we would like to work the other way around. For example: If I want a gain of -50dB on step 2, what resistor values for R_a and R_b do belong to that setting.
OK, based on this we can calculate the following formulas:
Therefore I made some calculations with a spreadsheet. Lets assume an inverted design with a feedback resistor of 220k and a resistor R_i on the negative input of 10k. Taking just the two into account we have a gain of 22 times (26 dB). Now take into account the rotary attenuator switch (R_tot = 22kOhms) and lets see how apart from the attenuation itself(!) the effective impedance changes the gain of the amp.
In the figure, we plotted the effective gain for a low-impedance source (e.g. CD-player) of 100 Ohms and a high-impedance source (tube preamp) of 2000 Ohms.
Finally, lets see how the ideal attenuation of just the switch changes in an inverted setup and what the resulting real steps in dB are when taking into account the variation in gain over the range of 12 positions. We do this by taking the gain (in dB) defined by the feedback loop above and add to it the dB attenuation by the 12-step switch.
The chart below shows how for any given attenuator with 12 steps gain in dB the required resistor values are highly dependent on the topology (inverted/non inverted) and the load on the input.
As shown above, if precision is your goal, the resistor values for inverted topologies differ significantly from the non inverted counterpart. The yellow line shows the behavior for non inverted designs, as a reference for how the same attenuator and the same resistor values in the feedback loop produce such different results in an inverted setup.
As to be expected, the gain of a non-inverted amp is dependent on the voltage divider made from R_a and R_b only and not dependent on the serial resistance of R_i and R_o. Therefore it's optimum values are far more linear than for the inverted setup as is shown by the yellow line in the chart above.

2.4b Alternative for Inverted amps

There is of-course several alternatives to the above solution. One would be to use a shunt design: One resistor permanently between input and ground. For the principle: Imagine in figure 2 above that the Rb side of the switch is not connected to ground.
Of course we need different values for the attenuator and therefore let's work out some formulas and maybe a new sheet entry in the spreadsheet.
<formula>

 


3. Building Attenuators

Now that we know how to calculate resistor values for a voltage divider, it's time to think about construction of the attenuator itself, the best switch to use, wiring, resistors etc. Below some examples are given for concrete applications.

What switch to use

Series Types

For my own gainclone designs I used cheap Lorlin switches so far. These switches are available from Conrad (Internet) and in shops. The website of Lorlin specifies several types of switches such as 6*2 or 12*1, in both shorting and non-shorting versions, with lugs or pins etc. Unfortunately, the non shorting (break before make) is the most widely used switch and is used for sources and output selection etc. For these applications a shorting version is hardly used and therefore shorting versions are hard to get. As the Lorlin switch is a closed design, it requires no maintenance and is self-cleaning (the inside only).
I found an open shorting switch in the conrad catalog (it is not advertised to be shorting but is definately is a shorting switch) and this one is easily modified to be useful for our application. Standard the switch does not have a stop and can be turned more than 360 degrees. With a very small drill and a bolt it is possible to modify the switch such that it becomes usable for an attenuator.
Anyway, should you be looking for 24-step switches or out-of-the-box shorting switches that are zombie proof etc. then alternative switches are available as well from antique, angela, reichelt etc.

Ladder Types

As shown on the right below there are some cheap alternatives for double deck switches, these will only cost a fraction of what a Dact switch will cost. These are of course 12-step switches and not the 24-step versions. However, for the average gainclone project this may just be good enough to work with.
As said, the Dact 24-step switches are amongst the best available. However, these switches are very expensive. Price differences between single of double deck switches is relatively low, so if you have room enough in your amp I would recommend to go for a double deck of 24 * 2 positions (sometimes incorrectly called stereo).

What Resistors to use

Metalfilm resistors do a better job here than carbon resistors is my experience. I have used Dale, Caddock and several types of metalfilm resistors. BC components (Philips) makes nice ones, but I do not hear much of a difference.
Then there is always the questionwhether carbon or metalfilm resistors provide the best sound in this application. As far as I'm concerned I would metalfilm resistors for an attenuator, but I like a clear and transparent sound. Carbon will make the sound slightly softer and if this is a design goal for you then by all means build your attenuator with carbon resistors. There is probably no good or bad only a matter of taste.

4. Examples

This section contains examples of attenators. The code in the subheaders refer to the corresponding worksheet in the spreadsheet found on the download page.

12-step series attenuator with shunt

 
 
Code
s12bn
Descr
Series 12-step break-before-make non-inverted
Project
Geenkloon
 
First, lets look at the 12-step switch made for GeenKloon. The first version made for Geenkloon was based on a switch which was non-shorting. This means that between two switch positions the wiper does not make contact with either contact. As a result, for a short moment there is not path from the wiper to either ground or signal in, and therefore the amplifier stage following the switch will see a non-defined impedance. Loud pops will result from your speakers and possibly cause damage.
Needless to say that these switches are not the first choice for building attenuators. But at the time I built Geenkloon I did not have an alternative and therefore I had to find a work-around.
The solution was simple: Connect a fixed resistor from the wiper to ground which will provide a defined impedance for the amp even between switch positions. And it's easy to live with the few drawbacks introduced by this design, the sound quality is very good.
Step
from
pin
to
pin
Resistors
(1/4W,1%)
dB
attn
dB step Impedance
1 (low) GND 1 wire infinite --
19,910
2 1 2 100 -45.98 --
19,910
3 2 3 270 -34.62 11.26
19,904
4 3 4 390 -28.37 6.11
19,885
5 4 5 750 -22.40 5.71
19,813
6 5 6 1,300 -17.01 5.02
19,592
7 6 7 1,100 -14.14 2.61
19,320
8 7 8 1,500 -11.32 2.55
18,842
9 8 9 2,000 -8.59 2.50
18,043
10 9 10 3,000 -5.63 2.85
16,566
11 0 11 3,900 -2.87 3.07
14,270
12 (hi) 11 12 5,600 0.00 4.33
10,451
19,910 45.98
Unfortunately I did not take the time to do calculations too carefully at the time, although in practise the attenuator works real well. That's the reason why I'll upgrade the geenKloon with an attenuator that is capable of playing less loud at lowest volume settings. Biggest problem being that due to the low value of the parallel resistor the impedance for high-volume setting drops significantly below the 20k. This makes the Geenkloon with this attenuator not really usable for tube sources.
Fortunately this can easily be corrected using another attenuator as described below, trying to get hold of the make-before-break (shorting) version of the Lorlin switch used for Geenkloon.

12-step series attenuator

 
 
Code
s12mn
Descr
Series 12-step make-before-break non-inverted
Impedance
22k7 (over full range)
Project
Geenkloon upgrade
This attenator will be used as a modification to the first version of the Geenkloon switch. This is really a very cheap 12 position switch that needs a little modification as the switch does not have a stop. It is however a make-before-break (shorting) switch and thus it's worth a little work in order to get a really cheap fnished product.
I described the modifaction process in some detail below for the double deck switch of the same manufacturer. It is a simple process, drill a small hole through one of the little dimples in the top plate and use a little bolt and fix it in the hole. The bolt needs to stick at least 1.5 mm through the hole on the innner side in order to provide a "stop" for the rotary switch mechanism inside.
Now you can solder the little resistors (1% types of 0.25W, matched per pair) on the small terminals. By using a layout at the outside of the swicth it's possible to make a quite elegant attenuator that can stand some mechanical use without intentional shorting once in a while.
Step
from
pin
to
pin
Resistors
dB
attn
dB step
Impedance
1 (low) GND 1
47
-53.69
--
22,729
2 1 2
82
-44.92
8.77
22,729
3 2 3
150
-38.22
6.70
22,729
4 3 4
330
-31.44
6.78
22,729
5 4 5
470
-26.47
4.97
22,729
6 5 6
820
-21.56
4.91
22,729
7 6 7
1,430
-16.69
4.88
22,729
8 7 8
2,400
-11.97
4.72
22,729
9 8 9
2,200
-9.15
2.82
22,729
10 9 10
3,300
-6.12
3.02
22,729
11 0 11
4,700
-3.09
3.04
22,729
12 (hi) 11 12
6,800
0.00
3.09
22,729



22,729

54.00

And after surgery of Geenkloon, the finished attenuator section looks like this:
The only drawback I can think of of this switch is it's open construction. But on the other hand with a little cleaning or eve better, regular use of the Geenkloon I do not anticipate any cracking or so. After all, I use small boxes for the clone without openings so dust and dirt will stay out under normal circumstances.

12-step series for Inverted Amps

 
 
Code
s12bi
Descr
Series 12-step break-before-make inverted
Project
Cyclone
The Cyclone project is an inverted amplifier. And therefore, the switch is part of the feedback loop of the inverted amp and the impedance will influence the gain (as does the voltage divider also).
How to use a non-shorting (break before make) switch in your amp? What I did is add a parallel resistor from the wiper which connects to the chip input, to ground. That parallel resistor will make sure that between the positions of the attenuator the input of the amplifier is in a defined state. For a 20K input impedance, a value of 47k or 100k would be nice, for a 50k attenuator I would use a 100k resistor. In general, use a resistor value at least 2 times the desired input impedance.
Important with the table below is to know that i used a parallel resistor of 47k and assumed an output resistance of the source device on the signal input of 100 Ohms, an input resistor of 10k and a feedback resistor of 220k for the inverted amp.
Step
from
pin
to
pin
Resistors
dB
attn
dB step Impedance
1 (low) GND 1
82
-49.35
5.94
23,724
2 1 2
82
-43.41
5.49
23,723
3 2 3
150
-37.92
5.92
23,722
4 3 4
330
-32.00
5.67
23,715
5 4 5
680
-26.33
4.73
23.688
6 5 6
1,200
-21.60
3.98
23.595
7 6 7
2,000
-17.62
2.83
23,327
8 7 8
2,400
-14.79
2.57
22.835
9 8 9
3,000
-12.23
2.57
21,994
10 9 10
3,900
-9.36
2.87
20,582
11 0 11
4,700
-5.71
3.65
18,487
12 (hi) 11 12
5,200
-0.14
5.57
15,766





49.35
As you can see, the resulting impedance as seen by the source device (CDplayer) is not constant but is between 15k8 and 23k7. But it stays above the 22k for most of it's range and in practise this is not a show-stopper.

Building a 12-step ladder Switch

 
 
Code
l12bn
Descr
Ladder 12-step break-before-make non-inverted, or a make-before-break type with grounding resistor on the opamp input.
Impedance
50k Ohms
Project
tbd, would fit Gainclone and Cyclone
For a ladder switch one needs a rotary switch with 2 decks. The wipers of both decks are connected with each other and with the input of the amp. For each of the 2 decks, the resistors are connected on 1 side with the switch contacts and are connected with each other and either ground or signal input on the other side.
The switch above and the one the right is a 12*2 switch. Although it's an open construction, which means cleaning once in a while in order to avoid corrosion or dirty contacts, it's build quality is excellent. And if you, like me, use the switch in an amp enclosure which is more or less air tight, corrosion will not play a large role anyway.
see screw in top plate
Only problem: Out of the box the switch does not have a stop (it's possible to turn it 360 degrees). But there is a work-around, and it's possible to fix the stop. Drill a small hole through one of the 12 marks/dimples in the top plate. Then us a little m1 bolt and screw it into place. Done. For just € 3.00 you made yourself a 2*12 switch that can be used to make a ladder attenuator.
Of course the switch can also be used to build a stereo version of a series attenuator, bit apart from the easy of use the technical construction is not different from the mono series attenuator described on this page and therefore not discussed further in this section.
However, in order to be protected even when the switch would degrade over time and would not be shorting in every position, I used a parallel resistor just in case. And unlike the series attenuator, for a ladder attenuator the parallel resistor does not cause the input impedance to vary over its range as long as you take its' value into account for every resistor pair on the ladder.
Look in the spreadsheet for examples of 50K attenuators (or any impedance value you choose yourself), the spreadsheet takes the optional parallel/shunt resistor into account and computes a ladder attenuator with 12 positions.
In this case I used a 100k parallel resistor which is effectively always in parallel with the resistor 2 in the table. Therefore, the voltage divider consists of the following resistors: Resistor 1 to signal in and the two Resistors 2 and the parallel resistor to ground.






Step
from
pin
to
pin
Resistor 1
Resistor 2
dB
attn
dB step Impedance
1 (low) GND 1
49,900
47
-60.53
--
49,947
2 1 2
49,900
82
-55.70
4.83
49,982
3 2 3
49,900
150
-50.47
5.23
50,050
4 3 4
49,900
240
-46.40
4.07
50,139
5 4 5
49,900
390
-42.21
4.19
50,288
6 5 6
48,700
787
-35.97
6.24
49,481
7 6 7
47,000
1,580
-29.76
6.21
48,555
8 7 8
47,000
3,160
-24.01
5.74
50,063
9 8 9
43,000
6,800
-17.29
6.72
49,367
10 9 10
37,400
16,000
-10.47
6.83
51,193
11 0 11
30,100
33,000
-5.63
4.84
54,912
12 (hi) 11 12
0
100,000
0.00
5.63
50,000






60.53

As you can see, even with the parallel resistor in place, the effective impedance is dependent on the resulting parallel resistance of R2 and the parallel resistor (therefore the value is 100K for the highest gain setting, as two resistors of 100k in parallel yield an effective resistance of 50k Ohms).

24-step series attenuator from old switches

 
 
Code
s24mn
Descr
Series 24-step make-before-break non-inverted
Project
tbd

Look at the geenkloon and Cyclone projects for serial attenators based on "cheap" Lorlin 12-position switches. As said above, especially with inverted Gainclones, care must be taken when selecting the resistor values.


It is possible to combine two single decks into one double deck and then make either a stereo series version or a mono ladder version.

5. More About the Spreadsheet

5.1 Why a spreadsheet program

Over the last months I received several requests for the spreadsheet or for additional information regarding the sheet. And based on the input I received I have made changes (hopefully improvements too) to the spreadsheet program.

5.2 This Excel program helps

I made this small Excel program that will help you in calculating the appropriate values for your own switch. It's easy to use and self-explanatory and allows the user to tweak every value by hand and see the results. The published value is based on non-inverted design and has versions for the following types of switches:
  • 24 step make-before-break (AKA shorting) switch for non inverted amps
  • 12 step make-before-break (AKA shorting) switch for non inverted amps
  • 12 step break-before-make (non shorting) switch for non inverted amps
  • 12 step make-before-break (non shorting) switch for inverted amps
Note: It does contains a setup for inverted topologies based on make-before-break switches. I'm still working on a version that helps better with break-before-make-inverted designs.
Download your version here: <Excel program Link>
The break-before-make variant in the sheet is a very cost effective way to build your 12-step attenuator with a cheap Lorlin switch of € 1.50 a piece and an additional shunt resistor from wiper to ground (to avoid damaging "plops").
Unless you're familiar with Excel, do not change the sheets because you might screw up the chart or other Excel references.

5.3 How to use the program

In order to work with the Excel program, a few decisions should be taken in order to choose the right sheet for your application.
  1. First of all, determine the type of switch you have, for my programs either a 12- or a 24- position switch. Also make sure you know whether it is shorting (or make before break) or non-shorting (break before make).
  2. If you have a lot of standard resistor values at home, or you want the program to only use a selected set of resistor values instead of the complete E96 range: Fill out the last sheet "e96 std values" and in particular the column D.
  3. Determine what steps you like for the various switch positions and fill them in in the appropriate column (on the screenshot it would be column D rows 9 - 19).


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The Matching Transformer

A matching transformer for a loudspeaker is just like one used to step up the output from a microphone, except that it is bigger, and designed to handle much more power. Suppose that a transformer is to match a 16-ohm loudspeaker to an amplifier requiring, not 16 ohms, but 6400 ohms, to which it is to deliver its power.
The impedance matching transformer permits input and output circuits to work into their proper impedances.
Suppose 9 watts are to be transferred. The formula for power is W = El, where W is power in watts, E is voltage in volts, and I is current in amperes. (Remember that the relation between voltage and current in a resistance is E = IR, where R is the resistance in ohms.)
Combining the two formulas, W = El = E X E/R = E2/R. Then by multiplying both sides by R» WR = E2. In the example, WR = 9 X 6400 = 57,600 = E2. Hence, E = 57,600 - 240 volts. Also I = E/R = 240/6400 = .0375 ampere.
At the voice-coil resistance, WR = 9 X 16 = !*4 = E2. Hence, E = Y144 = 12 volts. I = = 12/16 = 0.75 ampere.
But what would happen if a matching transformer were not used? The amplifier is only designed to deliver ,0375 ampere into a 6400-ohm resistance or load as it is called. If it is connected to 16 ohms, it will probably not deliver much more than .0375 ampere - maybe .05 ampere - and the waveform will be very distorted. When ,05 ampere is delivered to 16 ohms, the voltage is only E = IR = 16 X *05 = 0.8 volts, and the power delivered is only W = El = 0.8 X -05 = .04 watt, in place of the expected 9 watts!
The transformer reduces voltage by the turns ratio, increases current by the turns ratio, and multiplies impedance by the square of the turn ratio.
Notice what the transformer does: it reduces the voltage by the ratio of turns in the windings (called the turns ratio) and it also increases the current by the same ratio. It thus effectively multiplies the resistance (or impedance) connected to the secondary by the square of the turns ratio. In this case, the ratio was 20:1. The impedance connected to the secondary is multiplied by 20 X 20 = 400 (16 X 400 = 6400 ohms). The input voltage is 240 volts and the output is 12 volts; the input current is .0375 ampere and the output 0.75 ampere. The input and output power are the same (except for any losses due to the inefficiency of the transformer, which we have conveniently ignored; in practice, an output transformer would be more than 90% efficient, so this is no very great error).
Impedance matching. When the output transformer primary draws 0.0375 amp at 240 volts because the secondary draws 0.75 amp at 12 volts, the amplifier is effectively "connected" to a 6400-ohm voice coil.
When the amplifier supplies 240 volts to the "high" winding of the transformer, the core will be magnetized, and, due to its high inductance, very little current will be drawn from the amplifier, unless the voice coil is connected to the low winding.
The high winding must have 20 times as many turns as the low winding. This way, 240 volts induction in the primary will cause 12 volts in the secondary.
When the voice coil is connected across a 12-volt source, it will draw 0.75 ampere. If no current flowed in the primary of the transformer, this secondary current would destroy the induction by saturating the core, and the 12 volts (as well as the 240 volts) would disappear. To sustain the 12 volts, the amplifier must supply current to the primary to neutralize the effect of the 0.75 ampere in the secondary. As the primary winding has 20 times as many turns, it will only require one-twentieth the current, or .0375 ampere, to have the same effect and neutralize the effect of the secondary current.
Thus the transformer causes the primary winding to take .0375 ampere from the amplifier at 240 volts, when the secondary is connected to a voice coil of 16 ohms that takes 0.75 ampere at 12 volts. To the amplifier, it is the same as connecting a voice coil with a resistance of 6400 ohms, which it "wants," This is matching.
What would happen if the voice-coil resistance were 20 ohms instead of 16 ohms? If the transformer secondary voltage were still 12 volts, the voice coil would only take 0.6 ampere in place of 0.75 ampere. The turns ratio would still produce 240 volts across the primary winding, but the primary current required to balance the new secondary current of 0.6 ampere will be 0.6/20, or 0.03 ampere, in place of 0.75/20, or 0.0375 ampere. This is the same as if a load of R = E/I = 240/0.03 = ohms were connected to the amplifier directly. 8000 ohms is just 400 times the 20 ohms connected to the secondary winding of the transformer. The 20:1 turns ratio of the transformer thus always multiplies the resistance, or impedance, connected to its secondary winding by a factor of 400, or 20 squared (20*20).
Impedance matching permits maximum power output.
(a) Amplifier is matched to 16-Ohm speaker; amplifier sees correct 6400 ohms, output power is 9 watts.
(b) Amplifier is not matched to required 16-ohm, but 20-ohm speaker; amplifier "sees" now 8000 ohms, output power is 7.2 watts.


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Mengetahui Cara Belajar Ilmuwan Dunia

Menjadi kreatif di zaman modern saat ini sudah menjadi sebuah kewajiban. Suatu negara tentu akan menghadapi banyak masalah jika negara tersebut kurang memberdayakan sumber daya manusianya untuk bisa menjadi kreatif. Menjadi kreatif itu luas maknanya. Kreatif dalam berkarya, kreatif dalam berpikir bahkan berkreatif dalam menyelesaikan masalah.

Dalam belajar sains atau IPA, guru dan siswa seharusnya perlu mengenal latar belakang dari ilmuwan dan bagaimana mereka bisa menciptakan konsep ilmu/ suatu rumus. Dalam realita bahwa umumnya guru dan siswa juga mengenal konsep dan rumus dan proses pembelajaran kerap kali bercorak membahas rumus dan soal-soal saja. Sangat tepat rasanya kalau guru dan siswa juga mengenal proses kreatif para ilmuwan (seperti Albert Einstein, Thomas Alfa Edison, Isaac Newton, Charles Darwin dan lain-lain) dalam menemukan suatu fenomena lewat membaca buku biografi mereka.

1) Einstein, cara berbicaranya pada masa kecil tidak begitu menarik. Kemampuan berbahasa atau berbicaranya sangat lambat. Melihat kondisi itu orang tuanya sangat prihatin sehingga ia berkonsultasi dengan dokter. Karena kemampuan berbicaranya yang lambat membuatnya pernah gagal di sekolah dan kepala sekolah menyarankan agar ia keluar dari sekolah. Tentu saja ia memberontak kepada sekolah yang mengusirnya dan menganggapnya sebagai anak yang sangat bodoh.

Pada masa kecil, Einstein adalah anak yang baik dan ia punya karakter suka menolong, karakter ini membuatnya makin cerdas. Kemampuan berbahasanya memang lebih rendah dibandingkan kemampuan numerika atau matematika. Ia tidak pernah gagal dalam mata pelajaran matematika. Sebelum ia berumur lima belas tahun ia telah menguasai kalkulus diferensial dan integral yang dipelajarinya secara mandiri/ otodidak. Saat di sekolah dasar, dia berada di atas kemampuan rata-rata kelas, namun ia memiliki kegemaran untuk memecahkan masalah rumit dalam aritmatika terapan. Orang tuanya ikut mendukung minat Einstein dalam matematika. Ia membelikan buku-buku teks sehingga ia bisa menguasai pelajaran angka-angka selama liburan musim panas.

2) Thomas Alfa Edison, ia belajar bagaimana cara menemukan lampu. Sebelum lampu pertamanya menyala ia melakukan 5.000 eksperimen yang selalu berakhir dengan kegagalan. Namun cara berpikir yang dimiliki oleh Thomas Alfa Edison sangatlah positif dan tahan banting, ini membawanya kepada kreativitas tingkat tinggi.

3) Isaac Newton, lahir di Woolsthorpe- Lincolnshire,Inggris. Ia adalah seorang fisikawan, matematikawan, ahli astronomi, filsuf alam, alkimiwan, dan teolog yang berasal dari Inggris. Ayahnya yang juga bernama Isaac Newton meninggal tiga bulan sebelum kelahiran Newton. Newton dilahirkan secara prematur; Ketika Newton berumur tiga tahun, ibunya menikah kembali dan meninggalkan Newton di bawah asuhan neneknya.

Newton memulai sekolah saat tinggal bersama neneknya di desa dan kemudian dikirimkan ke sekolah bahasa di daerah Grantham dimana dia akhirnya menjadi anak terpandai di sekolahnya. Saat bersekolah di Grantham dia tinggal di-kost milik apoteker lokal (William Clarke). Sebelum meneruskan kuliah di Universitas Cambridge (usia 19), Newton sempat menjalin kasih dengan adik angkat William Clarke, Anne Storer. Namun Newton memfokuskan dirinya pada pelajaran dan kisah cintanya menjadi semakin tidak menentu/ putus begitu saja.

Keluarganya mengeluarkan Newton dari sekolah dengan alasan agar dia menjadi petani saja, bagaimanapun Newton tidak menyukai pekerjaan barunya. Kepala sekolah King’s School kemudian meyakinkan ibunya untuk mengirim Newton kembali ke sekolah sehingga ia dapat menamatkan pendidikannya. Newton dapat menamatkan sekolah pada usia 18 tahun dengan nilai yang memuaskan.

Newton diterima di Trinity College Universitas Cambridge (sebagai mahasiswa yang belajar sambil bekerja untuk mengatasi masalah keuangannya). Pada saat itu, kurikulum universitas didasarkan pada ajaran Aristoteles, namun Newton lebih memilih untuk membaca gagasan-gagasan filsuf modern yang lebih maju seperti Descartes dan astronom seperti Copernicus, Galileo, dan Kepler. Ia kemudian menemukan teorema binomial umum dan mulai mengembangkan teori matematika yang pada akhirnya berkembang menjadi kalkulus.

4) Charles Darwin lahir tanggal 12 Februari 1809 di Shropshire, Inggris. Ia anak ke lima Robert Waring Darwin. Ia belajar sesuai dengan kurikulum berbahasa Yunani Klasik. Ia tidak memperlihatkan prestasi yang banyak secara akademik. Kemudian ia mengambil jurusan kedokteran tetapi tidak banyak memperoleh kemajuan. Untuk itu ia melakukan usaha lain agar bisa maju. Ayahnya menyarankan Darwin untuk menjadi pendeta dan belajar di Christ’s College untuk belajar teologi. Tetapi ia juga tidak memperoleh kemajuan, ia malah senang berburu dan permainan menembak.Ternyata Darwin mempunyai minat dalam mengkoleksi tanaman, serangga, dan benda-benda geologi. Ia tertarik dengan bakat berburu sepupunya William Darwin.

Darwin mengembangkan minatnya dalam serangga dan spesies langka. Naluri ilmiah Darwin didorong oleh Alan Sedgewick, seorang ahli bumi, dan juga didorong oleh John Stevens Henslow, seorang professor botany. Darwin kemudian menjadi naturalist (pencinta alam) dan ikut melakukan ekspedisi dengan HMS Beagle. Tim ekspedisi HMS Beagle berlayar dan mengunjungi banyak negeri di lautan Pasifik Selatan sebelum kembali ke Inggris melalui Tanjung Harapan Baik di Afrika Selatan, dalam rangka mengelilingi dunia.

Darwin juga sangat dipengaruhi oleh pemikiran Thomas Malthus, dengan bukunya “Essay on the Principle of PopulationI”. Buku tersebut mengatakan bahwa populasi seharusnya bertambah sesuai dengan batas persediaan makanan, kalau tidak maka akan terjadi persaingan untuk memperebutkan makanan. Setelah membaca buku ini, Darwin memfokuskan teorinya bahwa “the diversity of species centered on the gaining of food – food being necessary both to survive and to breed”- semua jenis spesies terfokus dalam memenuhi kebutuhan makanan dan makanan berguna untuk kelangsungan hidup dan untuk berkembang biak.

Dari paparan di atas terlihat bahwa sukses seorang ilmuwan berskala dunia tidak jatuh dari langit, atau diperoleh saat kelahirannya. Kesuksesan sebagai ilmuwan diperoleh melalui proses kreatif (belajar kreatif) selama hidupnya.

Tidak semua orang memiliki kemampuan berganda yang hebat, Einstein misalnya pada masa kecil tidak beruntung dengan kemampuan bahasanya, namun ia mengembangkan kemampuan yang lain. Einstein bisa melejit pada bidang matematika. Bagi kita, mungkin bisa melejit pada bidang olah raga, musik, organisasi atau pada bidang lain.

Kesuksesan seorang anak juga akan terbentuk dengan dukungan orang tua seperti yang dialami Einstein, atau dukungan tokoh lain seperti yang dialami oleh Darwin. Tidak mungkin seseorang bisa sukses untuk skala nasional, apalagi untuk skala internasional kalau mereka tidak betah membaca. Newton membaca gagasan-gagasan filsuf seperti Descartes dan astronom seperti Copernicus, Galileo, dan Kepler. Darwin dipengaruhi oleh pemikiran (buku) Thomas Malthus, nah bagaimana dengan anda ? Orang bisa sukses karena memiliki karakter tidak mudah putus asa, Thomas Alfa Edison, misalnya, sangat tahan banting dan tidak suka mengeluh. Sebelum menemui sebuah lampu pijar yang bisa menyala, ia harus melakukan 5.000 kali eksperimen di bengkel milik ayahnya.

Bagaimana proses belajar kreatif para ilmuwan berskala internasional ?
Cukup simple yaitu miliki suatu bakat atau minat dalam bidang ilmu (misal dalam seni, fisika, kimia, sejarah, ekonomi, geografi, dll), kemudian kembangkan minat tersebut dengan belajar keras dan lakukan otodidak. Mintalah dukungan dari orang terdekat, termasuk guru. Miliki karakter yang tahan banting (tidak suka putus asa dan mengeluh), miliki minat dan kesenangan membaca yang mendalam untuk menambah wawasan. Untuk sukses maka diperlukan puluhan, ratusan atau ribuan kali latihan.


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Enam Fenomena yang belum terpecahkan

Kemajuan ilmu pengetahuan dan sains belum mampu menjawab semua pertanyaan di dunia, apalagi alam semesta. Sejumlah fenomena belum bisa dijelaskan secara nalar.

Seperti dimuat situs CNN, ilmuwan hingga saat ini belum bisa menjelaskan enam fenomena misterius, termasuk, bagaimana bisa Masjid Baiturrahim di Aceh bisa selamat dari musibah tsunami dahsyat 2004, sementara di sekitarnya porak poranda diterjang gelombang.

Berikut enam fenomena yang belum terpecahkan dan masih jadi pertanyaan besar.

1. Stigmata Padre Pio
Pada tahun 1918, seorang pastor muda yang sedang berlutut mendapati darah mengucur di tangan, samping tubuh, dan kakinya. Sebagian orang yakin luka yang ia derita adalah stigmata -- tanda ia tersentuh penderitaan Yesus di atas kayu salib. Sementara, beberapa lainnya beranggapan, ia melukai dirinya sendiri.

Meski dipermalukan dengan kontroversi itu, Padre Pio memutuskan meneruskan pekerjaannya, hingga ia mendapat reputasi sebagai penyembuh. Ia ditasbihkan menjadi Santo pada 2002. Saat upacara kanonisasinya di Vatikan, 300 ribu orang rela menerjang cuaca menyengat dan hadir untuk menghormatinya.

2. Fenomena susu ajaib Hindu
Pada 21 September 1995, seorang peziarah kuil New Delhi memberikan sesendok susu ke patung Ganesha, Dewa berkepala Gajah. Yang mengherankan, Sang Ganesha seakan menghisap susu itu.

Para ilmuwan berpendapat bahwa daya kapiler menyebabkan susu menyebar ke permukaan patung. Namun, dalam beberapa jam kemudian, sejumlah kuil Hindu dari Bangladesh hingga Canada melaporkan hal serupa: bahwa Dewa telah meminum susu persembahan mereka.

3. Keajaiban Masjid Baiturrahim
Ketika tsunami 2004 menerjang Banda Aceh, hampir semua bangunan di sekitar Masjid Baiturrahim rata. Gelombang tinggi juga menyapu masjid tersebut. Namun, masjid menara masjid berusia 123 tahun dan kubahnya tetap kokoh.

Umat muslim menganggapnya sebagai mukjizat, bahwa rumah Allah diselamatkan dari gelombang ganas tsunami.

4. Bagaimana asal-usul alam semesta
Dalam 80 tahun terakhir para ilmuwan berbaris di belakang Teori Big Bang yang muncul setelah Edwin Hubble pada 1929 menemukan miliaran galaksi di alam semesta adalah tidak menetap di tempatnya, melainkan bergerak menjauh satu sama lain.

Belakangan ilmuwan Stephen Hawking mengeluarkan teori kontroversial, bahwa Tuhan tidak ada hubungannya dengan penciptaan alam semesta. Kata dia, karena ada hukum seperti gravitasi, alam semesta bisa dan akan mencipta dirinya sendiri. Dan, hingga kini, tak satupun dari kita bisa memastikan bagaimana alam semesta tercipta.

5. Benarkah alien ada
Pernyataan bahwa, hanya penganut teori konspirasi yang percaya ada mahluk luar angkasa (ET), tidak sepenuhnya benar. Demikian pendapat Frank Wilczek, fisikawan pemenang Nobel di MIT.

Merujuk pada penemuan planet ekstrasolar, di luar tata surya kita yang serupa dengan Bumi, ia berpendapat, "Jika harus menebak, aku akan mengatakan ada ribuan, mungkin jutaan, mungkin milyaran planet di galaksi dengan beberapa bentuk kehidupan, dan mungkin ratusan atau ribuan yang memiliki mahluk cerdas seperti Bumi."

6. Berapa jumlah spesies di Bumi
Mungkin ada tiga juta, atau mungkin ada 100 juta. Para ilmuwan sepakat, jumlahnya lebih banyak dari angka 1,9 juta spesies Bumi yang sudah punya nama (sepertiga dari semua spesies di Bumi mungkin adalah kumbang tropis).

Salah satu alasan mengapa kita belum bisa mendapatkan hitungan akurat adalah bahwa sebagian besar dari makhluk di dunia amat sangat kecil. Dengan api teknologi baru, seperti sekuensing DNA akan memudahkan kita menemukan harta karun keanekaragaman planet kita.


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DitemukanPlanet yang mirip Dan lebih Besar dari Bumi

Para astronom telah menemukan sebuah planet yang sangat mirip dengan Bumi. Planet Ini adalah planet Bumi yang baru dan lebih besar dari bumi kita, dan lebih dari setengahnya tertutup oleh air. Dijuluki "Super Bumi", jaraknya sekitar 42 tahun cahaya dari bumi, dan berada di lain tata surya. radiusnya sedikit kurang 3 kali lebih besar daripada Bumi, dan memiliki orbit matahari sendiri, mataharinya sendiri lebih redup dan sekitar seperlima ukuran matahari bumi kita .

Super Earth dinamakan GJ 1214b, dan penemuannya adalah lompatan maju dunia astronomi yang telah mencoba untuk menemukan planet yang mirip dengan Bumi, dan yang dapat mendukung kehidupan. Suhu sebagaian planet ini, sekitar 200 derajat Celsius, tampaknya terlalu panas untuk mempertahankan hidup banyak orang, dan bahkan permukaan lautnya berselimut kabut gelap superheated steam dan gas-gas lain . Meskipun kondisi semacam ini tentunya dapat juga mendukung berbagai jenis kehidupan. Dari kepadatannya Planet ini juga menunjukkan bahwa permukaannya terdiri dari air dan es ¾, dan ¼ bebatuan.

Kedekatan kondisi alam dan permukaannya telah hamper mendekati dengan kondisi bumi ini merupakan penemuan yang menggembirakan semua orang dan membuat orang ingin belajar lebih lanjut tentang planet ini. Penemuan paling mirip sebelumnya adalah CoRoT-7b, tapi yang beredar. mengelilingi sebuah bintang Matahari lebih panas jauh lebih panas dari Matahari bumi kita.

David Charbonneau, kepala tim penelitian mengatakan, "Penemuan ini sangat menggembirakan Meskipun keadaan alam dan permukaannya yang mungkin belum begitu ramah terhadap kehidupan manusia, tapi mudah-mudahan setelah kita mampu mendaratkan kaki disana kita mampu membuat teknologi untuk kehidupa kita disana".


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