With the recent announcement of the world’s fastest Digital to Analog Converter (DAC) from Tektronix Component Solutions, i assumed it’d be interesting to wish a quick tutorial tour through one of the sole DAC architectures – the high voltage resistor ladder network as shown in Figure 1below.
The r-2r resistor ladder network converts a parallel virtual symbol/word into an analog voltage. Every digital enter (b0, b1, etc.) Provides its personal weighted contribution to the analog output. This community has some precise and interesting houses.
Scalable To Any Desired Number Of Bits
Makes use of best two values of resistors which convey smooth and accurate fabrication and integration.
Output impedance is capable R, regardless of the quantity of bits, simplifying filtering and further analog signal processing circuit design
Reading the r-2r network brings returned reminiscences of the limitless form of networks that you’re asked to unravel in the course of your undergraduate ee studies. The reality although, is that the analysis of this community and consequently the way it works simple. Via methodical application of thevenin identical circuits and superposition, we’ll display how the r-2r circuit works.
Let’s begin by analyzing the output impedance. Working through the circuit, simplifying it with Thevenin equivalents, makes this process simple. Thevenin says that if your circuit contains linear elements like voltage sources, current sources and resistors, that you simply can cut your circuit at any point and replace everything on one side of the cut with a voltage source and one series resistor. The voltage source is that the open-circuit voltage at the cut point, and thus the series resistor is that the equal circuit resistance with all voltage sources shorted.
Figure 2 below indicates the locations of the “reduce strains” we’ll use to simplify this circuit to calculate its output impedance. For this evaluation, the virtual inputs will all be taken into consideration shorted to ground.
The two 2R resistors to the left of the primary cut line in Figure 2 appear in parallel (when the digital bit b0 is grounded), and may get replaced with one resistor R as shown in Figure 3. The series combination of the 2 R resistors on the left of Figure 3 combine to one resistor useful 2R, which is in parallel with the 2R resistor to b1.
You may notice that this process repeats itself whenever we work from left to right, successively replacing combinations of resistors with their equivalents. As you’ll see in Figure 4, the circuit ultimately simplifies to one resistor R.
Thus, the output impedance of the R-2R resistor network is usually adequate to R, no matter the dimensions (number of bits) of the network. This simplifies the planning of any filtering, amplification or additional analog signal conditioning circuitry which will follow the network.
Next, we’ll inspect the thanks to calculate the analog voltage output for a given parallel digital input on the b0, b1, etc. inputs. We’ll use the same Thevenin equivalents technique shown above, also as Superposition. Superposition tells us that if you individually compute the contribution of a given source to the output (with all others voltage sources shorted and current sources opened), you’ll then sum the results for each of the sources to urge the last word result for the output.
We’ll calculate the contribution of two of the bits of our 4-bit R-2R DAC in Figure 5 to point out the method . We’ll assume the bits b0 and b2 are logic high, and bits b1 and b3 are logic low (ground).
We start by replacing the circuit to the left of the left-most cut-line with its Thevenin equivalent. Figure 6 shows the Thevenin equivalent, which is that the series resistor useful R (parallel combination of two 2R resistors), and thus the circuit voltage from the resistor divider (Vb0/2).
The process continues methodically, step by step for each cut-line, substituting the equivalent circuit for each stage, as shown graphically in Figure 7.
We can see that the voltage contribution from bit b0 is 1/16th of the logic high voltage capacitor. Each bit stage that this voltage passes through cuts the contribution by an element of two . you’ll begin to ascertain a topic here…
Next, we’ll compute the contribution from bit b2.
From the Thevenin equivalent analysis shown earlier, we all know that we will replace any portion of this circuit to the left of any of the cut lines with a resistor useful R, shown because the initiative in Figure 8. Next, we follow an equivalent Thevenin equivalent process to the output. As you’ll have already suspected, the contribution of bit b2 is just Vb2/4. Thus, the analog output voltage when bits b0 and b2 are adequate to logic one is just given by Vb0/16 + Vb2/4.
In a more general sense, the contribution of every bit to the output may be a simple binary weighting function of every bit. As you’re employed back from the MSB to the LSB, the voltage contribution each bit is cut in half. Thus, the overall sort of the equation to calculate the output voltage.
The R-2R resistor ladder based digital-to-analog converter (DAC) could also be an easy , effective, accurate and cheap because of create analog voltages from digital values. Monolithic R-2R resistor networks are available from various resistor component manufacturers, making it easy to incorporate them into your designs.