This blog is about a ladder. Another one.
A few days after I had finished the series of blogs I did on the R-2R resistor ladder I was in my local library, browsing the shelves in the way that you do, when I came across a book  on the history of the early days of analogue electronic music synthesizers - it was specifically about the Moog Synthesizer Co, though with lots of references to his main competitors: Bucchla, EMS, Oberheim and so on. It was an interesting read, though it focused on the business dealings and the composers and performers who used the equipment much more than the technicalities of the electronic design. I already knew that one thing that made the sound of his instruments very distinctive was the voltage-controlled filter that he designed but I didn't know that this was the one aspect of the design that was genuinely original and he was able to get a patent on it. Musicians liked it because it had a sharp cut-off and, through the use of feedback, could be peaky near the cut-off, even to the point of oscillation, so would produce lots of good sounds. One of the important things that came across from the book was that Moog did a lot of prototyping, experimenting, and what you might call general tinkering, and was designing stuff to sound good to his ears rather than merely meet a preconceived spec, though he was obviously a talented and clever design engineer too.
I was curious about how the filter worked, so when I got home I used the wonder of the internet to go off and find the original patent. The patent is here https://patents.google.com/patent/US3475623 and is worth a read.
Here's the schematic of his low-pass filter. As you can see, it's a lovely thing in the form of a ladder.
He explains in the patent how it works (the filter resistance comes from the transistor and varies in proportion to the collector current, which is what allows the cut-off frequency to be varied), but I thought it would still be interesting to look at the filter part of the low-pass version - the ladder - in the simulator to see how it behaves (I'm going to leave out the feedback that gives the resonant properties). Here is my version of the circuit. I've replaced his constant-current circuit controlled by an op amp (for voltage control of the cut-off frequency) with a simple current source. At the top of the ladder I'm using a voltmeter to measure the output (the difference between the two sides). In a practical implementation you'd need to follow it with a differential amplifier. The biasing I've done simply by guessing values and slapping them in - it doesn't seem to matter too much as long as the transistors are well enough spaced that the collector of each transistor has a bit of headroom in which to work [I checked what I had done with the DC analysis, and the voltages it reports for the nodes, to make sure everything was reasonable]. It required a fairly high supply voltage to accommodate all the intervals necessary in the ladder - I used 12V, which seemed to work ok.
Here's the frequency response with 1mA current through the tail of the differential amplifier
Here's the response with 100uA
And finally with 10uA
It works quite nicely [in the simulator] to control the cut-off point. The passband gain varies a bit with different control currents. The filter slope is 80dB per decade [24dB per octave], so it's a fourth-order filter (which we'd kind of expect from four RC filters in series - each RC stage giving 20dB per decade). It doesn't look like my component values will quite meet the three-decade range of frequency from 20Hz to 20kHz but they could probably be adjusted to do that.
All in all, a neat circuit and fun to play with. 'Thank you' Mr Moog.
 Analog Days: the Invention and Impact of the Moog Synthesizer. Harvard University Press 2002. Trevor Pinch and Frank Trocco.