Analog Design for the Digital World Class 1: Op Amps – Ideal, Reality, and Embedded November 17, 2014 Charles J. Lord, PE President, Consultant, Trainer Blue Ridge Advanced Design and Automation

This Week’s Agenda 11/17 Op Amps – Ideal, Reality, and Embedded 11/18 Resonant Circuits and Filters 11/19 Grounding and Shielding 11/20 A/D and D/A 11/21 Design and Test

This Week’s Agenda 11/17 Op Amps – Ideal, Reality, and Embedded 11/18 Resonant Circuits and Filters 11/19 Grounding and Shielding 11/20 A/D and D/A 11/21 Design and Test

We’ve had the Op Amp for a long time…

History of The Operational Amplifier Early electronic analog computers used sums, differences, multiplication, division, and even integration and differentiation of voltages to model real-world problems An array of accurate amplifiers to carry out these operations was needed. The first “Op Amps” were used in proprietary processes and applications…

The Norden Bombsight (WWII)

Postwar – the commercial Opamp The one we just saw was the first commercial modular opamp – Philbrick’s K2-W. It was differential input but the inverting input was used for a chopper. Vacuum tube amplifiers needed choppers to get the linearity needed. 1963 - μA702, the first IC opamp 1968 - μA741, first to include internal compensation 1972 – LM324, a long-standing standard

Differential Amplifier Model: Basic Represented by: A = open-circuit voltage gain vid = (v+-v-) = differential input signal voltage Rid = amplifier input resistance Ro = amplifier output resistance The signal developed at the amplifier output is in phase with the voltage applied at the + input (non-inverting) terminal and 180° out of phase with that applied at the - input (inverting) terminal.

Ideal Operational Amplifier The “ideal” op amp is a special case of the ideal differential amplifier with infinite gain, infinite Rid and zero Ro . and If A is infinite, vid is zero for any finite output voltage. Infinite input resistance Rid forces input currents i+ and i- to be zero. The ideal op amp operates with the following assumptions: It has infinite common-mode rejection, power supply rejection, open-loop bandwidth, output voltage range, output current capability and slew rate It also has zero output resistance, input-bias currents, input-offset current, and input-offset voltage.

The Inverting Amplifier: Configuration The positive input is grounded. A “feedback network” composed of resistors R1 and R2 is connected between the inverting input, signal source and amplifier output node, respectively.

Inverting Amplifier:Voltage Gain The negative voltage gain implies that there is a 1800 phase shift between both dc and sinusoidal input and output signals. The gain magnitude can be greater than 1 if R2 > R1 The gain magnitude can be less than 1 if R1 > R2 The inverting input of the op amp is at ground potential (although it is not connected directly to ground) and is said to be at virtual ground. But is= i2 and v- = 0 (since vid= v+ - v-= 0) and

Inverting Amplifier: Input and Output Resistances Rout is found by applying a test current (or voltage) source to the amplifier output and determining the voltage (or current) after turning off all independent sources. Hence, vs = 0 But i1=i2 Since v- = 0, i1=0. Therefore vx = 0 irrespective of the value of ix .

Inverting Amplifier: Example Problem: Design an inverting amplifier Given Data: Av= 20 dB, Rin = 20kW, Assumptions: Ideal op amp Analysis: Input resistance is controlled by R1 and voltage gain is set by R2 / R1. and Av = -100 A minus sign is added since the amplifier is inverting.

The Non-inverting Amplifier: Configuration The input signal is applied to the non-inverting input terminal. A portion of the output signal is fed back to the negative input terminal. Analysis is done by relating the voltage at v1 to input voltage vs and output voltage vo .

Non-inverting Amplifier: Voltage Gain, Input Resistance and Output Resistance Since i-=0 and But vid =0 Since i+=0 Rout is found by applying a test current source to the amplifier output after setting vs = 0. It is identical to the output resistance of the inverting amplifier i.e. Rout = 0.

Non-inverting Amplifier: Example Problem: Determine the output voltage and current for the given non-inverting amplifier. Given Data: R1= 3kW, R2 = 43kW, vs= +0.1 V Assumptions: Ideal op amp Analysis: Since i-=0,

Finite Open-loop Gain and Gain Error Ab is called loop gain. For Ab >>1, This is the “ideal” voltage gain of the amplifier. If Ab is not >>1, there will be “Gain Error”. is called the feedback factor.

Gain Error Gain Error is given by GE = (ideal gain) - (actual gain) For the non-inverting amplifier, Gain error is also expressed as a fractional or percentage error.

Gain Error: Example Problem: Find ideal and actual gain and gain error in percent Given data: Closed-loop gain of 100,000, open-loop gain of 1,000,000. Approach: The amplifier is designed to give ideal gain and deviations from the ideal case have to be determined. Hence, . Note: R1 and R2 aren’t designed to compensate for the finite open-loop gain of the amplifier. Analysis:

Output Voltage and Current Limits Practical op amps have limited output voltage and current ranges. Voltage: Usually limited to a few volts less than power supply span. Current: Limited by additional circuits (to limit power dissipation or protect against accidental short circuits). The current limit is frequently specified in terms of the minimum load resistance that the amplifier can drive with a given output voltage swing. Eg: For the inverting amplifier,

The Unity-gain Amplifier or “Buffer” This is a special case of the non-inverting amplifier, which is also called a voltage follower, with infinite R1 and zero R2. Hence Av = 1. It provides an excellent impedance-level transformation while maintaining the signal voltage level. The “ideal” buffer does not require any input current and can drive any desired load resistance without loss of signal voltage. Such a buffer is used in many sensor and data acquisition system applications.

The Summing Amplifier Since i-=0, i3= i1 + i2, Scale factors for the 2 inputs can be independently adjusted by the proper choice of R2 and R1. Any number of inputs can be connected to a summing junction through extra resistors. This circuit can be used as a simple digital-to-analog converter. This will be illustrated in more detail, later. Since the negative amplifier input is at virtual ground,

The Difference Amplifier Since v-= v+ For R2= R1 This circuit is also called a differential amplifier, since it amplifies the difference between the input signals. Rin2 is series combination of R1 and R2 because i+ is zero. For v2=0, Rin1= R1, as the circuit reduces to an inverting amplifier. For general case, i1 is a function of both v1 and v2. Also,

Finite Common-Mode Rejection Ratio (CMRR) A(or Adm) = differential-mode gain Acm = common-mode gain vid = differential-mode input voltage vic = common-mode input voltage A real amplifier responds to signal common to both inputs, called the common-mode input voltage (vic). In general, An ideal amplifier has Acm = 0, but for a real amplifier,

Instrumentation Amplifier NOTE Combines 2 non-inverting amplifiers with the difference amplifier to provide higher gain and higher input resistance. Ideal input resistance is infinite because input current to both op amps is zero. The CMRR is determined only by Op Amp 3.

The Four Amplifier Types Description Gain Symbol Transfer Function Voltage Amplifier or Voltage Controlled Voltage Source (VCVS) Av vo/vin Current Amplifier Current Controlled Current Source (ICIS) Ai io/iin Transconductance Amplifier Voltage Controlled Current Source (VCIS) gm (siemens) io/vin Transresistance Amplifier Current Controlled Voltage Source (ICVS) rm (ohms) vo/iin

Today’s trend – Opamp in a Micro Example: TI MSP430FG439

Today’s trend – Opamp in a Micro Example: Freescale K50

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Built-in Opamps PROS CONS Lowered chip count Board routing simpler Decoupling, power supply separation simpler Subject to μC limitations Specs may change with power modes Limited configurations For inputs, may want a more ‘robust’ IC

But what happens when we throw a little jω in the works? Tune in tomorrow!!!

This Week’s Agenda 11/17 Op Amps – Ideal, Reality, and Embedded 11/18 Resonant Circuits and Filters 11/19 Grounding and Shielding 11/20 A/D and D/A 11/21 Design and Test

Please stick around as I answer your questions! Please give me a moment to scroll back through the chat window to find your questions I will stay on chat as long as it takes to answer! I am available to answer simple questions or to consult (or offer in-house training for your company) c.j.lord@ieee.org http://www.blueridgetechnc.com