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I am reading Arts of Electronics and they are showing this circuit:

enter image description here

It says that D1 compensates for D2's forward drop by providing 0.6V of bias. I don't understand this circuit at all. Is the +5V an external 5v source? How does it compensate?

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The \$R_1\$, \$R_3\$ and \$D_1\$ circuit basically creates a 0.6V bias on the other side of the capacitor, so that a positive swing in the signal does not have to overcome a 0.6V hurdle. \$D_1\$ and \$R_3\$ form a shunt voltage regulator. The 0.6V voltage is conveyed to \$D_2\$ which is on the verge of conducting, as a result. So only a small positive upswing from the input is required to bring it to conduction. Because the input is capacitively coupled, it is pure AC. Its swings are additively superimposed on top of the bias voltage that exists on the other side of the capacitor. The 5V source is just from somewhere in the rest of the circuit. There is nothing special about it.

Perhaps you can get a different perspective by redrawing the circuit so that voltage falls from top to bottom. In this view, we highlight how the input is biased to 0.6V, but the output is 0.6V below that, down across the voltage drop of D1. So for instance suppose that the input creates a positive swing of 0.1V. This becomes 0.7V at the top of D2 (the whole point of the bias). At the bottom of D2, that swing is 0.1V again. D2 lets through enough current so that R2 has 0.1V across it.

A negative swing of 0.1V turns to 0.5V. But this cannot create a -0.1V output at the bottom of D2; that is nonsense because it is outside of our supply range. 0.5V is not enough to forward bias D2, and so the output is at 0V, pulled to ground by R2, which has almost no current flowing across it to create any voltage.

The purpose of R1 is to act as a flexible linkage to separate the reference 0.6 voltage, which is quite stiff, from the point where the signal is injected, which must on the contrary be free to swing about 0.6V. R1 also protects the diode from the input current swings. If we replace R1 by a wire, it won't work because the signal will try to move the voltage at the top of D1, whose cathode is pinned to ground. The input's positive swings will dump current through D1, abusing it. That creates a poor input impedance, resulting in an inability to generate the right voltage on or under D2.

On the other hand, if R1 is made large, the compensation diminishes, because the reference voltage is able to exert less control over the bias.

schematic

simulate this circuit – Schematic created using CircuitLab

To make it nicer for simulation, let us make the capacitor way bigger: 10 uF. Then we can use a nice, low frequency like 1000 Hz, which will not pass very well through a 100 pF capacitor into a less than 1K impedance. Also, let's hook up a signal source with a 3V amplitude. If you run the time domain simulation, you will see that the output waveform is quite precisely chopped in half.

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    \$\begingroup\$ Thank you very much for this thorough answer. I can't vote up yet because I don't have enough reputation. \$\endgroup\$ – Douglas Edward May 3 '13 at 11:22
  • \$\begingroup\$ @DouglasEdward You don't need to upvote him, hit the "accept answer" button to show that you used the information he gave. \$\endgroup\$ – Kit Scuzz May 6 '13 at 4:09
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    \$\begingroup\$ This is the most complicated circuit in The Art of Electronics to the point, I must say. Redrawing this circuit in presented form helps A LOT, but I still can't wrap my head around R1 resistor. Why there is no voltage drop across R1 and the bias voltage is conveyed to the input of D2? The only explanation I can think of is that no current flows through R1. Is that right? \$\endgroup\$ – Helbreder Apr 16 '14 at 8:21
  • \$\begingroup\$ "Pulled to ground by R2, which has almost no current flowing across it to create any voltage." I never thought of resistances as "voltage-making" devices depending on how much current flows through. Reading The Art of Electronics is one epiphany after another. Thanks @Kaz. \$\endgroup\$ – Jaime Gallego Dec 9 '16 at 18:36
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    \$\begingroup\$ @VanGo without R3, we put the 5V supply across diode D1. \$\endgroup\$ – Kaz Oct 30 '17 at 5:43
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I’ve been stuck by the same circuit and it uncovered a bunch of things that I didn’t understand in detail. So I’ll try to go very low-level in my explanation. If you notice anything wrong, please tell me and I’ll correct. Please also read the other answers, as they provide very valuable high-level insight.

First, make sure you understand diode voltage drop (if not google it). Diodes "consume" ~0.6-0.7V of your input, in other words, the voltage across the diode is ~0.6V. Since Voltage in series adds up, this means R3 sees ~4.3V (5V of the current source minus 0.6V of the diode).

schematic

simulate this circuit – Schematic created using CircuitLab

Next, we add a second path in parallel. This can be tricky to understand. e.g. Why would the current take the path with the resistors at all? But in the end, this is simple again: The diode takes 0.6V. R1 & R2 run in parallel to the diode, so they in total have 0.6V as well. Now they form a voltage divider, so we get \${1\over 11}\cdot 0.6V\$ across R1 and \${10\over 11}\cdot 0.6V\$ across R2.

schematic

simulate this circuit

To make things more complicated, there’s another diode in between R1 & R2. You could argue, that there’ll be another 0.6V drop across D2, which means across R1 & R2 will be 0V each, i.e. no current flowing at all. In practice Diodes will let some current through even before the 0.6V threshold is reached. If you simulate the circuit, it’ll calculate the drop to be only 0.4V with a current of 20μA. So there’ll be some very very small current going through the D2 side, while most of the current (4300μA or 99.5%) goes through D1. But as you can see, the point where SIG enters the circuit would in both cases still be at ~0.6V potential.

schematic

simulate this circuit

Now the final part to the puzzle is how the signal and 0.6V add to each other. In other words, how these two voltages become superimposed. I suggest to read up on how this works, if this is unclear, the following brief example illustrates the concept: You can consider the capacitor a voltage source and you calculate voltages for each source separately and add them up later.

schematic

simulate this circuit

So if 0.1V are discharged during the rising signal edge, the voltage potential will be 0.6V + 0.1V, the diode removes 0.6V of these, so the output only sees 0.1V again (minus neglectable minor voltages for the inaccuracies).

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The external 5V source via R3 produces about 0.6V on D1's anode. Ignore the input signal for now. The 0.6V level on D1 is transferred, via R1 to the anode of D2.

Because the cathode of D2 is connected to 0V via the 10k resistor, D2 is on the verge of conducting - this is where you need it to be for a semi-decent precision half wave rectification of a signal.

The signal arrives on D2's anode and all positive values will further enhance the forward bias of D2 hence the positive half cycle of the signal gets transferred to the output across R2.

Because D2 is on the cusp of being forward biased, any negative parts of the signal will reduce the forward bias of D2 and turn the device off thus, the negative half-cycles do not pass through D2.

A proper analysis would show a distortion (on the output waveform) around the mid-point of the signal but as a first approximation it will bear a reasonable resemblance to a precision half wave rectifier.

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    \$\begingroup\$ could you please explain why they used R1? Isn't there any voltage drop across R1 when bias voltage makes it through? \$\endgroup\$ – dirac16 Aug 13 '16 at 19:03
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    \$\begingroup\$ I really don't understand why +0.6V bias should move to D2's anode without any drop. What's really going on over there? \$\endgroup\$ – dirac16 Aug 13 '16 at 20:02
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    \$\begingroup\$ It goes to D2's anode because there is nothing to stop it. D2 won't stop it until it reaches about 0.6 volts and C cannot stop it because it blocks DC. The whole point is that the AC waveform is lifted by about 0.6 volts to put D2 on the verge of conduction at exactly the cetrepoint of the original AC waveform. Maybe download LTSpice (free) and simulate it. \$\endgroup\$ – Andy aka Aug 13 '16 at 20:27
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    \$\begingroup\$ OK Andy. I think that the +0.6V point is chosen to be a reference point for the D2's anode so whatever signal comes in from the capacitor would need to superimpose on top of the +0.6V reference point, hence 0.6+Vin sits on the anode. Am I right? \$\endgroup\$ – dirac16 Aug 14 '16 at 8:15
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    \$\begingroup\$ So it was sort of 'biasing' where we usually establish a predetermined voltage (or current) at a specific point in the circuit as a result of providing proper operating conditions in electronic components, here diode D2. Is it the best explanation for that? \$\endgroup\$ – dirac16 Aug 14 '16 at 10:34

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