4x4 Matrix Mixer - Impedance questions

[knutolai]

Hi guys!
So I'm working on a active 4x4 matrix mixer and I'm uncertain how I would go about calculate the input Z for the individual inputs.

Here's the schematic showing just a single input and output stage as well as the power section:


From my understanding the input Z of the inverting opamp buffers are 100k according to R1. Does the potentiometer at the input affect this? I've looked all over for matrix mixer and normal mixer circuits and the value ratio between P1 and R1 is all over the place. Some circuits suggesting a bigger P1, some set P1 and R1 equal, some set R1 bigger... 

What values would you guys suggest for P1 to keep the impedance at or around 100k?

Any and all replies are very appreciated!

[R.G.]

Look up Thevenin equivalent circuits.

Call the portion of the pot below the wiper Rb and the part above the wiper Ra. So the value of the pot is Ra+Rb for all positions of the pot.

The voltage on the wiper is always Rb/(Ra+Rb) times the voltage at the top of the pot.

Here comes the tricky part:
The voltage at the wiper appears to be in series with a resistor equal to Ra||Rb. So the impedance to a load after the wiper due to just the pot is 0 ( that is, the pot adds no series resistance to the voltage seen by the load on the wiper) to 1/4 of the pot value when the pot is in a position where Ra=Rb: the electrical middle, which is the same as half rotation for linear pots, but NOT for audio/log taper pots.

As they say on late-night infomercials, but wait! There's more!

The loading on the signal source connected to the top of the pot varies from the pot value, when the wiper is at ground, to the pot value in parallel with the opamp input when the pot position is at full up.


So for the setup you have, the loading on the input is 100K when the pot is at zero, to 50K when the pot is full up. In between, it's - in between.

[knutolai]

Oboy! Ill admit that took a while to dissect and digest, but yes I think I see how this works now.  Big thanks for the tip on Thevenin Circuits! It made it all comprehensible.

So for a circuit such as the one below the loading on each of the inputs is only ~9,1k when the pot is up all the way (10k||100k).

Sorry, didn't take the time to remove the image-text

From my understanding (having read Jack Orman's article on impedance http://www.muzique.com/lab/imp.htm) its favorable to have as high as possible input Z, and as low as possible output Z. This would be to avoid signal loss (leading to a lower signal-to-noise-ratio). What could be the argument for choosing a low value for P1, or is the circuit above just a example of bad design choice?

I have the feeling there is something important that I'm missing 

[R.G.]

The mixer in the schemo is designed for line-level inputs, which are generally assumed to be 1Vrms and from 600 ohms or lower source impedance.

The problem with guitar level work is that guitar pickups put out a signal of about 0.1Vrms and from an impedance of about 4K-8K resistive in series with a 2H to 4H inductor.

The inductor is what makes this tricky, as the SOURCE impedance for the guitar changes from maybe 10K at bass up to about 100K for 7KHz, which is about all the typical magnetic pickup puts out. A load that's not much higher than the about-100K number loses treble preferentially to bass, and sounds dull.

If a raw guitar - not a pedal! - is ever going into an input, the input needs to be about 1M or more to prevent treble loss. This is sometimes called "tone sucking" in guitar vernacular.

A pedal into one of the mixer inputs generally can drive 10K or 100K just fine, and more importantly, it has an impedance that's constant from bass to treble, so if it's loaded, it does not lose bass or treble preferentially, and can be fixed by turning up one or more gains.

[tubegeek]

What could be the argument for choosing a low value for P1, or is the circuit above just a example of bad design choice?

I have the feeling there is something important that I'm missing  

The phrase that you will often see in the input and output impedance context - which can be confusing - is "loading" and in this case "loading down the source."

The value of 10K is a dandy one WHEN THE SOURCE IS LOW IMPEDANCE, 1K or less. (RG did a good deed in carefully explaining the frequency-dependent source impedance that will be presented by a guitar pickup.)

The condition known as "bridging," which is desirable for best voltage transfer, means that the input impedance must be 10X the source impedance, and preferably larger. A ratio of 10:1 is sufficient for a signal loss of less than 1 dB and that is kind of the threshold for "good enough for audio."

When the ratio is closer to 1:1, we say that the input presents a "heavy" or "difficult" load to the source. This just means that the small input impedance is drawing a larger current from the source and also that we are losing signal voltage as compared to a bridged ratio of 10 or higher to 1.

Here's the part that may be counter-intuitive: when we speak of a "heavy load" it means a SMALL input resistance, not a LARGE one. The language can seem to suggest the opposite but it works the other way around.

When the input draws more current (due to the small resistance) the result is that the source will be required to provide a greater POWER to its load, which is the input. And this is a requirement that usually must be designed in specifically and can't always be counted on to be available. (You won't see op-amps on the output of power amplifiers as a rule.)

Here's the probable reason why the 10K value in the example mixer was not increased to a larger number: the larger the resistance at the input, the greater the noise contribution of the resistor itself.  So in a trade-off, 10K was deemed big enough but the choice was made not to go any bigger. The trade-off was made assuming that the source was NOT an impedance higher than 1K ohms. This assumption holds true for many, many audio devices, but not for a guitar pickup. And if it does hold and we want lowest noise in our mixer, we go for the just-big-enough value of 10K.

This is the reason we often discuss and use "buffer" circuits with respect to guitar - a buffer is a device that presents a very large input impedance to the source, and presents a very low source impedance at its output. I bet you can see why that is so common now!

In the case of the guitar as our source, we just have to live with a large resistor's larger noise contribution, unless we shell out the big bucks and create that large input impedance with a step-down transformer. But that has its own trade-offs, of course.

Good choice of project, by the way - I can't think of a circuit that is definitely buildable by a beginner, that will be more useful and will teach you more.

My advice would be: step one, either get a copy of Small Signal Audio Design by Douglas Self, or read up on the mixer projects at the Rod Elloitt ESP site, or, preferably, both. Next, build a module or two in such a way that you can replicate it easily but that you can change and adjust until you get it to your liking. Finally, carefully plan your physical layout so everything will fit and be easy to use before you start buying boxes and drilling holes. (Then start buying boxes and drilling holes.)

I think the only reason more people don't DIY mixers - especially a handy-dandy little one like this - is because the parts costs add up as you add capability and channels. But they are dead easy to make with op-amps and a little planning and if you source the parts carefully in decent-sized batches the cost won't kill you.

But then there's a lot of drilling, with no way around that.

[PRR]

> 10K is a dandy one WHEN THE SOURCE IS LOW IMPEDANCE, 1K or less.

Like a 150 Ohm microphone?

> is the circuit above just a example of bad design choice?

Looks fine to me, *for his application*.

We must consider level. Which gets into gain.

If you are coming right off a (mikcrophone or) guitar, buffering/boosting is "the right thing to do" before you do any other tricks. In old days this was expensive. Today a handful of TL072 and a +/-12V supply costs less than your knobs. Bring guitar into a 1Meg impedance, boost it 10X, *then* pot-down and mix-up. The TL072 can drive 2K fine (or four 10K pots with 100K mix-resistors). The 10X of gain brings the self-hiss of a guitar pickup well above the self-hiss of 100K mix-resistors.

OTOH, you don't always have to do "the right thing". I've mixed five guitars with 100K resistors in a passive mix-network into a standard instrument amp. With gain set for good playing results, the "silent" hiss was audible; but 5 guitarists together don't stay silent for long. Plenty good enough for classes.

[knutolai]

Great responses people! Thank you

The 10X of gain brings the self-hiss of a guitar pickup well above the self-hiss of 100K mix-resistors

So choosing a too high mixing resistor when its not necessary can actually add internal component noise into the signal? Could you recommend any articles (or just search-words) on this? This seems to be the main point I´m missing.

OK so I was thinking of expanding the project to include a op amp voltage follower on each input similar to this one:


This would be to make the mixer more suitable also for devices with bigger output impedances. This way I could lower the value of the potentiometers as the output impedance from the voltage follower is very small.

Edit: added new/tentative schematic below. Notice R2 is now 240k, meaning that above 180 degrees (3'o clock) rotation of the potentiometers the signals are amplified.



I think its time to bring out the breadboard. I´ll try put up a buildreport when I'm done

[blackieNYC]

If the pots are larger than 10k (which is just 10% of the 100k that follows), then turning down one channel (to ground) will have a greater effect on the impedance at the summing point of the mixer.  If you had 100k pots, turning one down would affect the levels of the other channels significantly, wouldn't it?  I have tried it, I think the simple mixer works quite well for pedals. Are you mixing guitars?  I guess I'm assuming you are mixing FX

[R.G.]

If the pots are larger than 10k (which is just 10% of the 100k that follows), then turning down one channel (to ground) will have a greater effect on the impedance at the summing point of the mixer.  If you had 100k pots, turning one down would affect the levels of the other channels significantly, wouldn't it? 

Not quite. The impedance at the opamp end of the 100k resistors is about zero, driven to what's called a 'virtual ground' by the feedback action.

In fact, the summing of currents into the virtual ground at the inverting input is why this setup is so popular - one input's pot setting cannot have any significant effect on the others, regardless of the pot values.  The mixing may get odd, but they won't interact to any noticeable degree.

[blackieNYC]

Ah - vg.  -thanks, RG.  I'm about to box up this very mixer.  It will be mixing pedals (fx loop blend). Are you saying I should go for higher value pots?  I posted once about the seemingly ubiquitous choice of 10k pots on all the common mixer schematics ( in stompbox land, so we're generally talking pedal sources), in the same sites that have so much info on input impedance design.  Should I address the pedals' ability to drive this mixer?  I can get 100k pots.  Better? Or theoretically better?

[R.G.]

Higher or lower value pots are an issue of what drives them. This will follow the rule of thumb that you want the driven thing to have an impedance 10x or more higher than the driving thing, so you lose little signal voltage.

So the question when mixing pedals is "what's the highest output impedance of any pedal that's going to be plugged into this?"

In very crude generalities, pedals can drive a 10K pot just fine. In turn, the "output impedance" of a 10K pot maxes out at about 2.5K, so a mixer-input resistor of 25K or more is a negligible load on it. But as always, the devil is in the details.

Some pedals have 100K output level pots. I don't remember any with 500K or 1M output level pots, but they may exist. The "output impedance" of a 100K pot maxes out at 25K, so a 250K mixing resistor would pass the "negligible loading" criteria.

But as long as you're already up at nearly line level, or being driven by an active device like a pedal, things get more subtle and complex.

First, if the pedal has its own output level pot, you could logically assume that you don't need an input level pot on your mixer at all. This simplifies the hardware, but makes operating the mixer more complex as you have to remember to adjust the mix out on the pedals, not on the mixer at all. Putting a pot in the mixer for each channel is also somewhat complicated, as now both the pedal and mixer will adjust the mix.

Second, you may not have to worry about loading so much. The reason loading is critical for pedal inputs is the variation of output impedance of a guitar pickup with frequency. It has a higher impedance as frequency goes up. So if you load it, the loading is disproportionately on the highs, and you lose treble. For a pedal output with what is probably a resistive output impedance, you may load it down, but you will likely load down all frequencies equally, so the tonal balance is not lost, only some level. You may be able to easily up the level with the pedal output level pot, so losing some voltage to loading may not matter much, certainly not like with a guitar pickup.

What this boils down to is that you have to know your sources. If you'll ever stick a raw guitar output into a mixer channel, it would be wise to make that input impedance be 1M or greater; this is probably better done with a buffer. Opamp buffers are very non-coloring right up until they start having signal outputs that clip. JFET and other simple buffers have slight distortion at nearly all levels, even before clipping. But some people *like* the slight distortion. So *if you have a buffer* and *what kind of buffer*  matter.

If you know you'll *never* have a guitar plugged in directly, it gets simpler. You probably don't need buffers.  And since active devices, the outputs of pedals, are the only inputs, and since these are relatively low impedance, and since in any case they're not going to upset the tone balance if loaded, the choice of a mixer pot value is somewhat arbitrary.

You may choose to not have a mixer pot at all if all of your devices will have their own level pot. You can probably use 10K, 50K, 100K, maybe even 250K interchangeably for the mixer input pot, with decent results.

The mixer resistor is a balance. The lower the resistance, the lower the thermal noise. But you're already introducing thermal noise with the mixer opamp, and the real difference between 10K, 100K, and 250K in non-microphone-level work is not all that big. The resistors inside the pedals matter more because of any pedal gain.

I'd say - pick one. 10K, 50K, 100K, they'll all work all right IF YOU'RE ONLY GOING TO PLUG PEDALS INTO IT.  If you will ever plug a guitar into it, I'd advise using a buffer in front of each input. Or put one or two inputs which have a buffer, and build in a toggle or slide switch for bypassing the buffer.  I did this for the most recent series of pedals in my day job; they're buffered or non buffered, you pick. This covers the issue of whether a buffer is needed, or if not needed is somehow causing metaphysically-induced signal-badness.

And, reaching this point, you'll notice that the box, the layout, the jacks, pots, knobs, and switches dominate the appearance, size and cost.

[knutolai]

Are you mixing guitars?  I guess I'm assuming you are mixing FX

I will probably use it for FX for the most part, creating feedback-loops and stuff. However I want this mixer to be usable for stuff like guitars and piezo-microphones too. You could easily use a matrix mixer to send your guitar through different effects in parallel.

What this boils down to is that you have to know your sources. If you'll ever stick a raw guitar output into a mixer channel, it would be wise to make that input impedance be 1M or greater; this is probably better done with a buffer. Opamp buffers are very non-coloring right up until they start having signal outputs that clip. JFET and other simple buffers have slight distortion at nearly all levels, even before clipping. But some people *like* the slight distortion. So *if you have a buffer* and *what kind of buffer*  matter.

Are there any other disadvantages of having input buffers when all devices connected is at line level? The extra cost is quite minimal compared to the rest of the necessary components, and couldn't the possible clipping be avoided by adding extra headroom (18 volt supply)?
EDIT: searching for "overbuffering" gives a article that states that buffers has a SNR of 2-4%. Also too many not-too-transparent buffers would color the sound. I guess I'm answering my own question here..  

[tubegeek]

You've got it: raise the supply to add headroom, but more stages cost you a small noise penalty.

[knutolai]

So I'm still waiting for the components and got to thinking about the values of R1-4. The output Z from the input-buffers should be round 10 Ohm according to Jack Ormans website. Same goes for the buffers in the output stages. So wouldn't it make sense, component-noise-vice, to lower the values, say, by a factor of 10 (at least) as the Output-Input Z ratio, from one module to the next, doesn't really need to exceed 1:1000?
Edit:

Think I found my answer here! Rod Elliott actually has a Matrix Mixer project: http://sound.westhost.com/project129.htm