TLDR; capacitor C180 was added to the circuit below to make it happy.

Background: 24V PLC digital signal driver (spec: up to 15mA sourced or sunk, 100kHz, idiot proof vs shorted field wiring, able to tristate for troubleshooting by integrators). The driver IC I had been using became unavailable amid this year’s supply chain trainwreck. I thought, no problem, just throw down a few transistors.

The driver is shown below, omitting a couple of ESD/TVS protection and termination parts. SIG_VCC is the “24V” supply. The logic input comes from a 5V circuit, and in that case SIG_VBB is 2.5V. The input does level-shifting and passes on the tristate condition, or close enough for PLC purposes.

Without C180, among other things, there was cross-conduction from delayed turn-off (caused by dV/dt on the output pushing/pulling current through the output transistor’s base-collector capacitance — pretty much Miller effect). Other fixes would be to cascode, or to drive the output transistors harder, neither of which were attractive in this project. Adding C180 looks like it cleans it up reasonably well with a single component. When the inputs transition, this cap pushes/pulls current in the opposite direction from the unwanted current associated with the Miller effect. If C180 is sized right, the result is a much nicer looking trapezoidal voltage waveform on the output. (Assuming with some capacitive loading, which was ensured by some of the output-protection parts not shown.)

And here’s another convenient falstad simulation to play with, which isn’t entirely true to life, but can show the cross conduction effect going away.

A general SISO control loop and equivalent closed-loop transfer function expressions are shown in Figure 1. F(s) and G(s) are complex frequency domain transfer functions. Assuming they can be expressed as a ratio of polynomials, we decompose them into numerators and denominators with F = N_F / D_F and G = N_G / D_G

The numerators contain the zeros, and the denominators contain the poles. The expression on the rightmost side of Figure 1 then has a useful implication: We can move poles and zeros between F and G, while keeping the denominator of the closed-loop expression constant. Because the denominator is responsible for the stability of the loop, this means we can, in the abstract, keep the stability properties constant, but change how many zeros we have (including none at all).

Next, let’s break F into (H)(P), where P is our “plant”, i.e. the physical system we cannot change, and H is under our control. Typically, the controller in the forward path. This is shown in Figure 2. For the closed-loop expression, simply substitute F=HP into the Figure 1 expression..

The reverse path, G, is typically just an immediate sensor reading of the output. I.e. G=1. Two observations here. First, any poles added to the reverse path will create a closed-loop zero per Figure 1. This may be undesirable. Second, if our control expression has zeros, we may prefer to place them into G rather than into H, again to avoid creating closed loop zeros.

Next, let’s look at a common loop rearrangement trick. Figure 3 shows another loop configuration.

Here the (input-output) passing through H is mixed with the (output) passing through C, before going into plant P. We can convert between the forms in Figure 2 and Figure 3 as follows:

This can allow us to get a “free zero” without doing any differentiation, when H contains an integrator, as is common.

Most simply, if H=1/s (an integrator), and C is a constant, G = (H+C)/H = (1+Cs), i.e. a single zero. Since the equivalent G is in the reverse path, this zero will not show up in the closed loop expression.

More elaborately, if H=1/s and C=(1+s/z)/(1+s/p) , G will have two zeros and a pole at the origin. Only one zero will appear in the closed loop expression.

This can have some minor advantages when constructing single loops. In cascaded loops it can be relevant because the noise gain of the outer loop contains the closed loop gain of the inner loop. Now we have a way to remove a zero from that inner-loop’s closed loop expression (at the expense of increasing a gain elsewhere however).

Shooting for 0.5 to 2MHz range. Haven’t built it yet.

falstad link (pictured below)

Doing this as kind-of an exercise to play around with transistors.

• 5V single supply
• output range 1V-3V(ish)
• one current into resistor controls amplitude
• another current into capacitor controls ramp rate
• frequency is proportional to the ratio of the two currents
• voltage level controlled by V_bot input (should be buffered coming in)
• headroom: bottom about 1V, top is whatever the current sources require (probably diode drop + emitter resistor)

Reference: Both the 2-comparator hysteresis section, and the current-switching section, come from a Dennis Feucht book excerpt on triangle wave circuits that was published in EE times, lots of problems solved in there!

[ note to self, previous overly complicated design (falstad), included makeshift transistor buffer, just to experiment with a transistor buffer. file away somewhere else ]

analog thing, 0 to almost 90 deg, falstad simulation

PLL, almost 0 to almost 180 deg, falstad simulation (I think it’s possible to add counter/divider to this to extend phase range)

• Learned about this neat sine wave circuit on Friday, apparently from the 60’s. Considered for a project later this year that’ll need a cheap 2-decade-adjustable sine wave? nah not clear that it’s better than the alternatives.
• On Sunday night, finally got around to making a cheezy simulation of this current source, or (my original intention) like this.
  • I am hoping to fashion a two-terminal-device out of two Nagata mirrors (also from the 60’s) feeding back on each other.
  • Reference: the Nagata mirror is commonly called the “peaking current source”, and the concept has been extended by Wyatt (90s) and Hirano (2016).
  • I need to figure out how it actually works, and whether this is any better from getting gain with an emitter resistor. I also didn’t think it would self-start, but the simulation says it does.
  • A better simulation is a good idea also. Will definitely return to this.
  • To be clear, the 2-terminal application I am thinking of is totally reinventing the wheel, of the LM334 two-terminal current source, and it’s also of limited use because of the temperature coefficeint, but it’s fun.