I’m working on a nice project, a Linkwitz’s idea. I’m working on his PLUTO speaker system which is great and easy to DIY, I’m reading the whole site and I have found a very interesting proposal along with pluto’s electronics.
I have been analyzing all parts and I thought that would be really neat to write something about each one of them. I’m not going to use LM3886 ICs, instead I will use LM1875, therefore my project is smaller and also a slightly different than his. I should start from the PSU, instead of that I will start writing about its input buffer, filters (crossovers) and power amp section, and after that I will focus on PSU. You may wonder why LM1875? Well simple, because I already have those, and because i love them. And most important because I live in an apartment, so I do this for my neighbors’ sake.
Well, let’s talk about buffering, one thing i find a pretty neat trick is the abilty for Hi and Lo Level Inputs, and I will focus on these two options, because I will use them , below there’s a standard input buffer with Hi and Lo inputs.
- Fig 1 – Input buffer circuit
Let’s examinate the Low Level Input first. We can simplify this circuit above, then, by the following schematic.
- Fig 2 -Low Level Input buffer
On the very first stage we found a High Pass Filter (F HP1), made by C3 with R5 and R6, assuming that C3 >> C4, therefore C4 with R6 and R5 make a Low Pass Filter (F LP1). For fh1, fh2, fl1 and fl2 calculations (cutoff frequencies at -3dB) we do the following:
Given: R5, R6 and fhp1 (high pass frequency cutoff)
- Eq 1.01 – Calculation for C3
if R6 >> R5, then we can assume:
- Eq 1.02 – Simplified calculus for C3
Given a flp1 (low pass freq cutoff)
- Eq 1.03 – Calculus for C4, given a R6 and flp1
Then we calculate buffer gain, Av, and after that we calculate its cutoff frequencies. We have to take into account that dB gain for power signals is given by: A[dB] = 10 * LOG(Ap), therefore in order to find out this fc at -3dB, we need to assume that Av[-3dB] => Av/(2)^0.5. So, Av[dB] = 20 * LOG(Av) , and Av[-3dB] = 20 * LOG(Av * 0.707)
From Fig 2 we get this forumla:
- Eq 1.04 – Op Amp gain formula
Now we have another stage, OA stage, with its gain as shown above, but it also has pasive components, same as its input stage as a low pass and a high pass filters. And that makes it to behave as a bandpass filter. So we can evaluate and calculate all variables involved, but first there are some considerations before picking up components values. We should consider two options to understand how this circuit will work on frecuency domain. First f>0Hz (low freq) and after that f>>0Hz (high freq). But first let’s consider the following schematic, for our calculus purposes.
- Fig 3 – Equivalent non inverting circuit
From the schematic above, we can get the following:
- First considerations for Frequency response analisys
First case when f is almost0Hz, low frequency signal input, that means a few decades of Hz and we consider C1 connected therefore Xc1 > 0ohms. And due to small value of C2, its impedance is very high and has no effect upon R4 , therefore:
Eq 1.06 - Calculus of Rx and therefore Xc1 and C1
Same criteria goes for C2 calculation. Now we’re talking about higher freq, fc>>0Hz, therefore we must consider that Xc1=0ohms, but Xc2 is not infinite anymore, and has influence on R4, then the amplifier’s gain changes as well. In order to estimate its cutoff frequency, we must find (again) its transfer function (G(s)) and its poles, then analyze them in frequency domain aspect.
Eq 1.08 - Calculus for C2
And that’s it, for now. This is how we can set all parameters for an input buffer, of course this is only one part, the low level input on my next post i will talk about the high level input, that means that I will only talk about how it behaves due to all these parameters found here. There will be no search for Caps or Resistors values at all. But maybe we can come into a compromise with all calculated and estimated values here and there.
Finally i leave you with a spreadsheet that makes all these calculations easier, fields in yellow background are values we must enter.
- Sistemas de Control Automático – Cap 9: 9-1-2 Especificaciones en el dominio de la frecuencia, pag. 543 – Benjamin Kuo.
- and of course, Linkwitz’s website.
Thanks, until next update.