Non-Inverting Amplifier

A non-inverting amplifier connects the signal directly to the positive input of an op-amp, giving the same phase at output as input and an extremely high input resistance. Sensor interfaces and instrumentation front-ends use it precisely because it does not load the source.

Core Concept

In the non-inverting configuration, the input signal drives the positive terminal directly. The op-amp's output feeds back to the inverting input through the voltage divider formed by Rf and R1. This negative feedback forces the inverting input to track the non-inverting input, making the voltage at the inverting input equal to Vin.

Since the inverting input sits at Vin, and R1 connects it to ground, the current through R1 is Vin/R1. This same current flows through Rf. The output voltage must be Vin + (Vin/R1) × Rf, which simplifies to Vout = Vin × (1 + Rf/R1). The gain is always greater than or equal to 1.

The input resistance is extremely high, ideally infinite, because the signal connects to the op-amp's non-inverting input, which draws no current. In practice, for LM741, it is around 2 MΩ differential, much larger than a typical source impedance.

Key Equations

Closed-loop gain: Acl = 1 + Rf/R1. Always positive, always at least 1.

Input resistance (ideal): Rin = infinity. Practical value for LM741: ~2 MΩ.

Output resistance (ideal): Rout = 0 Ω.

Bandwidth: BW = GBP / Acl. For TL071 with GBP = 3 MHz and Acl = 10, BW = 300 kHz.

Unity gain configuration (voltage follower special case): Rf = 0, R1 = infinity => Acl = 1

Given:
  R1 = 4.7 kΩ
  Rf = 56 kΩ
  Vin = 0.2 V DC
  Op-amp: TL071, GBP = 3 MHz
  Find: Vout, closed-loop gain, bandwidth

Why this formula:
  Non-inverting configuration gives Acl = 1 + Rf/R1

Formula:
  Acl = 1 + Rf / R1
  Vout = Acl × Vin
  BW = GBP / Acl

Substitution:
  Acl = 1 + 56,000 / 4,700 = 1 + 11.91 = 12.91
  Vout = 12.91 × 0.2
  BW = 3,000,000 / 12.91

Calculation:
  Acl ≈ 12.91
  Vout = 2.58 V
  BW = 232,378 Hz ≈ 232 kHz

Final Answer:
  Closed-loop gain = +12.91 (non-inverting)
  Vout ≈ 2.58 V
  -3 dB bandwidth ≈ 232 kHz

Exam Tip: GATE often asks to distinguish gain formulas between inverting and non-inverting configurations. Inverting gives Acl = -Rf/R1 and Rin = R1. Non-inverting gives Acl = 1 + Rf/R1 and Rin = very large. A frequent mistake is applying the inverting formula to a non-inverting circuit. Also, the minimum gain of a non-inverting amplifier is 1, not 0.

Key Properties

• Gain is always positive (no phase inversion) and always ≥ 1 for a standard non-inverting configuration.
• Input resistance is the op-amp's own differential input impedance, typically 2 MΩ for LM741 and much higher for JFET-input TL071.
• Setting Rf = 0 Ω and removing R1 (open circuit) gives the unity-gain voltage follower, also called a buffer.
• The feedback factor β = R1/(R1 + Rf), and closed-loop gain Acl = 1/β when open-loop gain is large.
• Bandwidth reduces as gain increases; TL071 at a gain of 30 has a bandwidth of 3 MHz/30 = 100 kHz.
• For precise gain, use 1% metal-film resistors; 5% carbon film introduces gain error of up to 10% in worst case.

Quick Revision

• Acl = 1 + Rf/R1; always positive, minimum value is 1.
• Input resistance is very high (ideally infinite); does not load the source.
• Output is in phase with input (0° phase shift).
• BW = GBP / Acl for a given op-amp.
• Voltage follower is the special case: Rf = 0, Acl = 1.
• Feedback factor β = R1/(R1 + Rf).
• Use 1% resistors for predictable, stable gain values.
• Exam trap: students write Acl = Rf/R1 for the non-inverting amplifier, omitting the +1 term, which is wrong at low gain values where the +1 is significant.