Solving a Diode Circuit: Output Voltage & Resistor R Values

[dobry_den]

Homework Statement

A scheme of a diode circuit is attached. The voltages at the inputs A and B are 5V.
A. What is the output voltage (=voltage at the black node, Z)?
B. What values of resistance would you recommend for the resistor R?

2. The attempt at a solution
A. The diodes D₁ and D₂ are reverse biased (the voltage on the anode is less than the voltage on the cathode). So the output voltage should be (5V - voltage drop across the resistor).

B. Since this is a diode AND gate and both inputs are equal to logical 1 (5V), the output should be also logical 1. That means its value should approach 5V. This is the case when the voltage drop across the resistor is low -> thus its resistance should be low.

Could anyone, please, comment on my solution. Is it correct? Do you know what the standard resistance of the resistor R is?

 

[berkeman]

Well, with 5V on both anode and cathode, the diodes are technically at zero bias, not reverse bias. Remember the diode equation that we were discussing in your other threads.

The value of the output resistor in a circuit like this is a tradeoff between power consumption and speed. Can you tell me a little about that tradeoff, and what value of resistance (and resulting currents) might be a good compromise for a logic circuit?

 

[dobry_den]

Well, i thought there had to be a lower voltage on anode than 5V since there's a resistor between the 5V voltage supply and the diode..? Why aren't you taking its voltage drop into account?

And to the value of resistance - isn't the output voltage the most important thing? A high value of resistance would alter the output voltage to such an extent that its value might be interpreted incorrectly by another circuit connected to the output - it might get out of the "logical 1" voltage interval. This is the way I understand diode logic. Maybe the problem's here..?

 

[berkeman]

No load is shown at point Z, so no current flows through R. If there is a load at Z, then yes, there would be some voltage drop from the output current flowing through the load.

And you are correct that too large a value of output resistance R would result in too big of a voltage drop through R, and corrupt the output logic "high". So you probably wouldn't pick a value of 100kOhms for most logic circuits. But you also wouldn't pick a value of 10 Ohms, since that would result in really big currents being drawn for no good reason.

The main real-world consideration is the speed of the edges that result at the output of the circuit when changing from low-to-high, and high-to-low. Assuming that the signals that drive A and B are pretty strong, which would be the slowest output transition at Z -- low-to-high, or high-to-low? Why?

And assuming an output capacitance of 20pF (pretty typical for looking into a following gate's input capacitance plus PC board trace capacitance), what would the maximum value of R be if you wanted to be sure that you could pass a 10MHz square wave through this diode-AND circuit with reasonable fidelity?