Electronics: Operational Amplifiers

• These notes cover Electronics & Digital Systems, specifically AMET-121, Week 8.

Agenda Topics

• Operational amplifiers in aerospace applications
• Operational amplifiers in general
• The ideal op-amp
• Practical op-amps
• Internal block diagrams of op-amps
• Differential amplifiers
• Differential and common-mode signals
• Common-Mode Rejection Ratio (CMRR)
• Op-amp parameters
• Negative feedback
• Op-amp circuits with negative feedback
• Input and output resistance for inverting and noninverting amplifiers
• Voltage-followers
• Op Amp applications.

Operational Amplifier Basics

• An operational amplifier (op-amp) features two input terminals: inverting (-) and noninverting (+), plus one output terminal.
• Op-amps typically need two DC supply voltages, one positive and one negative, which are often omitted from schematic symbols for simplicity.

Ideal Op-Amps

• Ideal op-amps have optimum characteristics, not achievable in reality, but actual op-amp circuits can approximate the ideal.
• Ideal op amps have infinite voltage gain and input resistance, with zero output resistance.
• Op-amps have inverting and non-inverting inputs, related by the phase of input and output signals.

Practical Op-Amps

• Practical op-amps have limitations, including power and voltage limits.
• A practical op-amp still has high voltage gain and input resistance, but only low output resistance.
• Op-amps have inverting and non-inverting inputs related by the phase of input and output signals.

Internal Structure of Op-Amps

• Op-amps are made of three amplifier circuit types: differential, voltage, and push-pull amplifiers.

Differential Amplifiers

• Most op-amps use a differential amplifier ("diff-amp") as their input stage.
• Differential amplifiers offer advantages like common-mode noise rejection.
• In single-ended mode, the input signal applied, the signal at the collector of Q1 is inverted, while the signal at the collector of Q2 is not.
• At the emitters of transistors Q1 and Q2, the signal is one-half of the input signal's magnitude.

Differential and Common-Mode Signals

• Signals are applied to one or both inputs of the device.
• Two input signals out of phase constitute differential-mode operation.
• Signals in phase, represent common-mode operation.
• The outputs cancel and approach zero when the inputs are in phase.
• The outputs are amplified to exceed the input when the inputs are out of phase.

Common-Mode Rejection Ratio (CMRR)

• Noise sources often induce unwanted voltage in signal lines.
• Differential amplifiers cancel noise induced in common-mode, but signals in differential mode are not rejected.
• Common-mode rejection ratio (CMRR) measures the ability to reject common-mode signals: CMRR = Avd / Acm, where Avd is differential mode gain and Acm is common mode gain.
• CMRR can be expressed in decibels (dB) as: CMRR = 20 log(Avd / Acm).
• Example: For a diff-amp with a differential voltage gain of 500 and a common-mode gain of 0.1, the CMRR is 5000, or 74 dB.
• Example: A diff-amp has Ad = 100 and a CMRR of 90 dB, input is a 50 mV differential signal, and a common mode noise of 1.0 V is present.
  • The differential signal is amplified by 100, resulting in a signal output of 5.0 V.
  • The common-mode gain of 0.0032, this amplifies the noise by 0.0032 resulting in: Vnoise = Acm × Vin = 0.0032 × 1.0 [V] = 3.2 mV.

Op-Amp Parameters

• Input bias current (IBIAS) is the average of input currents needed to bias the amplifier's first stage: IBIAS = (I1 + I2) / 2.
• Differential input resistance is the total resistance between inverting and non-inverting inputs.
• Common-mode input resistance is the total resistance between each input and ground.
• Input offset current (IOS) is the absolute difference between the two bias currents: IOS = |I1 - I2|.
• Output resistance is resistance viewed from the output terminal.
• Common-mode input voltage range is the range of input voltages that, when applied equally to both inputs, don't cause clipping or distortion.
• Common-Mode Rejection Ratio (CMRR) is the ratio of differential gain to common-mode gain; the differential gain equals its open loop gain.
• Slew rate is the maximum output change rate in response to a step input voltage.
• Example: For an output signal that goes from -10 V to +10 V in 25 μs, the slew rate is 0.8 V/μs.

Negative Feedback

• Harold S. Black in 1921 realized that returning some output back to input in opposite phase would cancel distortion, one of electronics' important concepts.
• When a feedback network returns some output to the inverting input of the op-amp's differential amplifier stage, only the difference signal (Vin - Vf) gets amplified.

Op-Amp Circuits with Negative Feedback

• Negative feedback stabilizes gain, reduces distortion, and increases input resistance in almost all linear op-amp circuits.
• In a noninverting amplifier configuration, difference between Vin and Vf is minimal due to feedback, giving a formula of Vin ≈ Vf.
• The closed-loop gain is controlled by feedback resistors, the closed-loop gain for the noninverting amplifier is: Acl(NI) = 1 + (Rf / Ri).
• Inverting amplifiers ground the noninverting input (sometimes via a resistor for bias balance).
• The inverting input is nearly at ground, referred to as a virtual ground due to feedback.
• The virtual ground looks like ground to voltage, but not to current
• For the inverting amplifier, the closed-loop gain is: Acl(I) = -Rf / Ri.

Input Resistance with Noninverting Amplifiers

• The input resistance (Rin) of an op-amp without feedback is used.
• For the 741C, the manufacturer specifies Rin at 2 MΩ.
• Negative feedback increases this.
• Rin(NI) = (1 + AolB)Rin, where Aol is the open-loop gain, and B is the feedback factor.
• This high value makes the input resistance considered infinite for practical applications.
• The Rin(NI) is large, a DC bias path is still required because the op-amp is a DC amplifier.

Output Resistance with Noninverting Amplifiers

• The output resistance of an op-amp without feedback is Rout.
• Negative feedback reduces this by a factor of (1 + Aol / B).
• The resistance is approximated as zero for practical uses.
• In equation form Rout(NI) = Rout / (1 + AolB).
• Aol is the Open Loop Gain.
• Low output resistance implies the output voltage remains independent of the load resistance, assuming current limits are not exceeded.
• Example, the op-amp has: 𝐴𝑜𝑙 = 100,000, 𝑅𝑖𝑛 = 2 𝑀Ω, 𝑅𝑜𝑢𝑡 = 75 Ω with components of 𝑅𝑓 =36 kΩ , and 𝑅𝑖 = 1.5 kΩ:
  • 𝐴𝑐𝑙(𝑁𝐼) = 25.
  • 𝐵= 0.04.
  • 𝑅𝑖𝑛(𝑁𝐼) = 8 𝐺Ω.
  • 𝑅𝑜𝑢𝑡(𝑁𝐼) =.019 Ω.

Input Resistance with Inverting Amplifiers

• Negative feedback aims to keep the inverting input close to the AC ground for the inverting amplifier configuration.
• Input resistance equals the input resistor (Ri).
• Expressed as Rin(I) = Ri.
• Low input resistance presents a disadvantage in this circuit.
• Rin(I) equals Ri, it's user-adjustable to support specific value requirements.

Output Resistance for the Inverting Amplifier.

• Parallels the noninverting amplifier setup: Rout(I) = Rout / (1 + AolB).
• Although Rout(I) is minimal, an op-amp's ability to drive certain loads is limited.
• For the 741C model, the typical limit is 20mA.
• For the example, a value can be calculated to be Acl(I) = -24.
• Given Ri is 1.5kΩ, this means tThe input resistance is = 𝑹𝒊 = 𝟏. 𝟓 𝒌𝜴.

Voltage-Followers

• It constitutes a unique instance of a noninverting amplifier, characterized by a gain (Acl) of 1.
• In this configuration, negative feedback boosts input resistance.
• Negative feedback also serves to curtail output resistance.
• This configuration suits interfacing a high-resistance source with a low-resistance load.