dacr2r
As known there are two types DAC using R-2R ladder. One is voltage output and another is current output. The voltage output type has a constant output impedance which equal to R. The current output type has a input code dependent output impedance. Then how the output impedance dependent on the input code? Are there a mathematical function, such as $$R_{out} = f(n)$$ in which n is the input code, to show this?
Refs:
You need to AC-Couple the signal. Just put a capacitor in series.
Usually, the current spec of a output pin is so that positive values denote current flowing out of the pin. This should be clearly defined in the datasheet.
In your case, it's obvious the pin is sinking current, meaning this "center current" is flowing into the pin. Given no other information, this is what you'd expect from the negative value, but it's also clear that is what is what is expected by the example circuit. The opamps are connected as inverting transconductance amplifiers, with current flowing into the D/A pin causing positive output. The voltage of these D/A pins will be held at 0 by the opamp circuits.
Best Answer
The output of a current-output R-2R ladder must be connected to a virtual ground, such as the inverting input of an opamp whose non-inverting input is grounded. Call the feedback resisor RF.
You can think of the circuit overall as "amplifying" the fixed VREF with a variable gain that is equal to
$$A = -\frac{R_F}{R_{OUT}}$$
and
$$V_{OUT} = -V_{REF}\frac{R_F}{R_{OUT}}$$
We know that
$$I_{OUT} = \frac{n}{2^N} \cdot \frac{V_{REF}}{R}$$
and
$$V_{OUT} = -R_F \cdot I_{OUT} = -R_F \cdot \frac{n}{2^N} \cdot \frac{V_{REF}}{R}$$
It's easy to set these two equations equal to each other and solve for ROUT:
$$-V_{REF}\frac{R_F}{R_{OUT}} = -R_F \cdot \frac{n}{2^N} \cdot \frac{V_{REF}}{R}$$
$$R_{OUT} = R \frac{2^N}{n}$$
When the input code is all-zeros, none of the R-2R legs are connected to the output node, so ROUT is infinite. When the input code is all-ones, ROUT is nearly equal to R.
It really doesn't matter, though, since as we said before, this output node needs to be connected to a virtual ground, so ROUT is in parallel with an impedance that is effectively zero. It's actual value has no effect on the rest of the the circuit.