Amplifiers

Question 1

Difference-amp CMRR test
Part: INA826, G = 10, –40 °C → +125 °C
Goal: prove CMRR ≥ 80 dB at 1 kHz.

Answer 1

Step 1 Hook-up
+15 V |
1 kHz 10 Vpp sine ── both inputs (tie together)
Output monitor AC-coupled to scope (50 Ω)

Step 2 Measure
Vout_AC = 1 mVpp (observed)
Vcm_in = 10 Vpp
CMRR = 20 log (Vcm_in / (Vout_AC / G))
   = 20 log (10 / 0.1) = 100 dB → pass
Step 3 Over-temp check
INA826 spec: 100 dB min → 94 dB @ 125 °C → still > 80 dB → OK

Question 2

Noise density hand-calc (op-amp version)
Circuit: OPA211, G = +10, Rs = 1 kΩ, BW = 20 kHz, 25 °C

Answer 2

Step 1 Grab numbers from datasheet
en = 1.1 nV/√Hz, in = 1.7 pA/√Hz, IB = 100 nA

en = input-voltage noise density = 1.1 nV/√Hz (at 1 kHz)
in = input-current noise density = 1.7 pA/√Hz (at 1 kHz)
IB = input bias current = 100 nA (typical, 25 °C)
GBW = gain-bandwidth product = 45 MHz
G = closed-loop gain = +10 (set by external resistors)

Step 2: Thermal noise of Rs
Er = √(4kTRS) = √(1.66×10⁻²⁰ × 1 kΩ) = 4.0 nV/√Hz
(Er = thermal-noise voltage-density created by source resistor Rs)

Step 3: Current-noise voltage across Rs
Ein = in × Rs = 1.7 pA × 1 kΩ = 1.7 nV/√Hz
(Ein = voltage-density produced by input-current-noise in flowing through Rs)

Step 4: RSS input-referred noise density
En_in = √(en² + Er² + Ein²) = √(1.1² + 4.0² + 1.7²) = 4.5 nV/√Hz
(En_in = total input-referred noise-voltage density after RSS summation of en, Er, and Ein)

Step 5: Output RMS noise
En_out = En_in × G × √BW = 4.5 nV × 10 × √20 000 = 0.64 µVrms
(En_out = RMS noise voltage at the op-amp output after amplifying En_in by gain G and integrating over noise bandwidth BW)

Question 3

Q3. Anti-aliasing filter design
ADC: 16-bit, fs = 1 MSPS, want –3 dB @ 200 kHz, –40 dB @ 500 kHz (Nyquist).

Answer 3

Step 1 Choose fC
fC = fs / 5 = 200 kHz (gives 2.5× margin)

Step 2 Required attenuation
–40 dB in one octave → 2nd-order Butterworth meets –40 dB @ 500 kHz

Step 3 Component values
Set R = 1 kΩ, then
C = 1 / (2 π R fC) = 1 / (6.28 × 1k × 200k) = 796 pF → use 820 pF

Step 4 Verify
-3 dB: 200 kHz
-40 dB: ≈ 500 kHz → OK

Step 5 Op-amp buffer
Choose GBP ≥ 5 × fC → ≥ 1 MHz; OPA211 (GBP = 45 MHz) → no phase error