Current Switching DAC The circuit in Figure P4–88 is a 4–bit digital-to-analog converter

(DAC). TheDAC output is the voltage vO and the input is the binary code represented by bits b1, b2, b3, and b4.

The input bits are either 0 (low) or 1 (high), and each controls one of the four switches in the figure.When bits are low, their switches are in the left position, directing the 2R leg currents to ground. When bits are high, their switches move to the right position, directing the 2R leg currents to the OP AMP’s inverting input. The 2R leg currents do not change when switching from left to right because the inverting input is a virtual ground (vN¼vP¼0). The purpose of this problem is to show that this constant-current switching produces the following input-output relationship.

(a) Since the inverting input is a virtual ground, show that the currents in the 2R legs are i1¼VREF/2R, i2¼VREF/4R, i3¼
VREF/8R, and i4¼VREF/16R, regardless of switch positions.

(b) Show that the sum of currents at the inverting input is b1i1 þ b2i2 þ b3i3 þ b4i4 þ iF ¼ 0 where bits bk (k¼1, 2, 3, 4) are either 0 or 1.

(c) Use the results in parts

(a) and

(b) to show that the OPAMP output voltage is

as stated.

Transcribed Image Text:

RF vo 2R VREF b1 + b +