Digital Control Systems Waseem Gulsher BS (Evening) 4 Dec, 17 Digital to Analog Conversion Methods Lecture – 11 Digital Control Systems Waseem Gulsher

Applications of Op-Amp

Inverting Amplifier There are two basic circuit configurations employing an op amp and two resistors: the inverting configuration, and the non-inverting configuration 1.#

Open loop mode Vo = AoL ( v2 – v1) inverting output non-inverting Op-amp circuit symbol Open loop mode Vo = AoL ( v2 – v1) AoL is referred to as the open loop gain. Notice that is v2 = v1, the open loop gain equals to 

Example An ideal op-amp, was measured in a lab experiment in open-loop mode. Determine the open loop gain (AoL) and complete the table below which shows the results of the experiment.

Applications of Op-Amp Op amp can be configured to be used for different type of circuit applications: Inverting Amplifier Non – inverting Amplifier Summing Amplifier Integrator Differentiator

Two main characteristics: We want the open loop gain to be equal to  which means that v2 = v1 We also want the input resistance to be equal to  , hence there is no current going into the op-amp

Inverting Amplifier

Example # 2 Gain = - (R2 / R1) = -(150/12) = -12.5

Non - Inverting Amplifier

Non - Inverting Amplifier

Voltage Follower / Buffer Amplifier Vo = Vi Hence, gain = 1

Summing Amplifier i1 + i2 + i3 – i4 – 0 = 0

Integrator  

Differentiator  

Example # 3 NON - INVERTING INVERTING INVERTING Va Vb Calculate the input voltage if the final output, VO is 10.08 V.  Then: Vb = -(5/5) Va -0.504 = - Va Va = 0.504 V Have to work backwards: Vo = -(100/5) Vb 10.08 = -20 Vb Vb = -0.504 V Finally: Va = (1 + 10/5) V1 0.504 = 3V1 V1 = 0.168 V

Binary-Weighted Input DAC

Binary-Weighted Input DAC 4-bit DAC with binary weighted inputs. 1.#

Binary-Weighted Input DAC Each of the input resistors will either have current or no current depending on the input voltage level. If the input voltage is zero, the current is also zero. If input voltage is high ,the amount of current depends on the input resistor value and is different for each input resistor. 1.#

Binary-Weighted Input DAC Since there is practically no current into the op-amp inverting (-) input, all of the input currents sum together and go through Rf . Since the inverting input is at 0v,the drop across Rf is equal to the output voltage ,so Vout = If Rf . The values of the input resistors are chosen to be inversely proportional to the binary weights of the corresponding input bits. The lowest value resistor (R) corresponds to the highest binary weighted input (23). 1.#

Binary-Weighted Input DAC The other resistors are multiples of R (R, 2R, 4R and 8R) and correspond to the binary weights of 22 , 21 , 20 . Thus the output voltage is proportional to the sum of binary weights because the sum of the input currents is through Rf . 1.#

R/2R Ladder DAC

R/2R LADDER DAC 1.#

R/2R LADDER DAC Assume that D3 input is high (+5 v) and the others are low(0 V) .This condition represents the binary number 1000. Essentially no current goes through the 2R equivalent resistors because the inverting input is at virtual ground. Thus all the current (I= 5V/2R) through R7 also goes through Rf and the output voltage is -5V. 1.#

R/2R LADDER DAC The op-amp keeps the inverting input near 0V because of negative feedback. Thus all current goes through Rf rather than into the inverting input. 1.#

R/2R LADDER DAC 1.#

R/2R LADDER DAC Previous Figure shows the equivalent circuit when the D2 input at +5V and the others are grounded. This condition represents 0100 , i.e.2.5V in series with R. This results in a current through Rf of I = 2.5V/2R , which gives an output voltage of -2.5V. 1.#

Performance Characteristics of DAC

Performance Characteristics of DAC Resolution : The resolution of a DAC is the reciprocal of the number of discrete steps in the output . For example a 4-bit DAC has a resolution of one part in 24 -1 = 1/15*100 = 6.67%. 1.#

Performance Characteristics of DAC Accuracy: Accuracy is derived from a comparison of the actual output of a DAC with the expected output. It is expressed as a percentage of a full-scale or maximum output voltage. If a converter has a full-scale output of 10v and the accuracy is +/- 0.1% ,then the maximum error for any output voltage is (10V)(0.001) = 10 mV 1.#

Performance Characteristics of DAC Linearity: A linear error is a deviation from the ideal straight-line output of a DAC. Monotonicity: A DAC is monotonic if it doesn’t take any reverse steps when it is sequenced over its entire range of input bits. Settling Time: Normally defined as the time it takes a DAC to settle within +/- ½ LSB of its final value when a change occurs in the input code. 1.#

Performance Characteristics of DAC Example: Determine the resolution, expressed as a percentage, of the following: a. an 8-bit DAC b. a 12-bit DAC Solution: a. For the 8-bit DAC, 1/28-1 *100 = 1/255*100=0.392% b. For the 12-bit DAC, 1/212-1 *100 = 1/4095*100=0.0244% 1.#

Assignment # 3 Example: 8.4 Cont…. 1.#

Assignment # 3 What is the value of Vin1 from the figure above? 1.#

Thank You