4.3 Operational Amplifiers, Active Filters & Instrumentation Bioamplifiers

Operational Amplifiers, Active Filters & Instrumentation Bioamplifiers

Human physiological bioelectric signals—such as the electrocardiogram (ECG: $0.5\text{ to }4.0\text{ mV}$), electroencephalogram (EEG: $10\text{ to }100,\mu\text{V}$), and electromyogram (EMG: $1.0\text{ to }10\text{ mV}$)—are extremely low in amplitude and originate from high-impedance biological tissue interfaces. These fragile signals are surrounded by massive environmental electromagnetic interference, primarily $120\text{ V}_{\text{RMS}},/,60\text{ Hz}$ capacitive displacement fields from hospital mains wiring. The Certified Biomedical Equipment Technician (CBET) must master operational amplifier (op-amp) theory, instrumentation bioamplifiers, and active filtering circuits that extract clean diagnostic waveforms from noisy clinical environments.

---

1. Operational Amplifier Characteristics: Ideal vs. Real-World Devices

An operational amplifier (op-amp) is a high-gain DC-coupled differential voltage amplifier with two inputs (Inverting input, marked $-$, and Non-Inverting input, marked $+$) and one single-ended output.

+-----------------------------------------------------------------------------+
|                        THE OPERATIONAL AMPLIFIER                            |
|                                                                             |
|                              +Vcc (Positive Supply Rail)                    |
|                                   |                                         |
|   Non-Inverting (+) -----\       |                                         |
|                           \------+                                          |
|                            \     |                                          |
|                             \    |----+---- Output (Vout)                   |
|                             /    |    |                                     |
|                            /-----+                                          |
|   Inverting (-) ---------/       |                                         |
|                                   |                                         |
|                              -Vee (Negative Supply Rail)                    |
|                                                                             |
|   Transfer Function:  Vout = A_OL * ( V_+ - V_- )                           |
+-----------------------------------------------------------------------------+

Comparison Table: Ideal vs. Real Medical-Grade Op-Amps:

The Two Golden Rules for Op-Amps with Negative Feedback:

When negative feedback is applied from the output to the inverting input terminal (and the op-amp output is not saturated against the supply rails):

1. Golden Rule 1 (Virtual Short): The differential voltage between the two inputs is zero ($V_+ = V_-$). The op-amp drives its output to whatever voltage is required to force the inverting terminal voltage to match the non-inverting terminal.
2. Golden Rule 2 (Zero Input Current): The input terminals draw zero current ($I_+ = 0\text{ A}$ and $I_- = 0\text{ A}$) due to extremely high internal input impedance.

---

2. Standard Op-Amp Negative Feedback Topologies

+-----------------------------------------------------------------------------+
|                      BASIC OP-AMP CIRCUIT CONFIGURATIONS                    |
|                                                                             |
|   [1. INVERTING AMPLIFIER]             [2. NON-INVERTING AMPLIFIER]         |
|             Rf                                   Rf                         |
|         +--/\/\/--+                          +--/\/\/--+                    |
|         |         |                          |         |                    |
|   Vin -/\/\/--(-)  |                     GND -/\/\/--(-)  |                 |
|       Rin     \   |                              Rin  \   |                 |
|                >--+-- Vout                             >--+-- Vout          |
|       GND ----(+)                               Vin --(+)                   |
|                                                                             |
|   Vout = -Vin * (Rf / Rin)             Vout = Vin * ( 1 + Rf / Rin )        |
|                                                                             |
|   [3. UNITY GAIN BUFFER]               [4. DIFFERENCE AMPLIFIER]            |
|         +---------+                                  R2                     |
|         |         |                              +--/\/\/--+                |
|         |     (-) |                              |         |                |
|         |      \  |                        V1 --/\/\/--(-)  |               |
|         +------ >-+-- Vout                     R1      \  |                 |
|                /                                        >--+-- Vout         |
|   Vin --------(+)                          V2 --/\/\/--(+)                  |
|                                                R3      |                    |
|   Vout = Vin (Av = 1.0)                               /\/\/ R4              |
|   Zin = High, Zout = Low                               |                    |
|                                                       GND                   |
+-----------------------------------------------------------------------------+

Circuit Gain Formulations:

1. Inverting Amplifier:
   • Current through $R_{\text{in}}$ equals current through $R_f$: $\frac{V_{\text{in}} - 0}{R_{\text{in}}} = \frac{0 - V_{\text{out}}}{R_f}$
   • Closed-Loop Gain: $A_v = \frac{V_{\text{out}}}{V_{\text{in}}} = -\frac{R_f}{R_{\text{in}}}$
   • Input Impedance: $Z_{\text{in}} = R_{\text{in}}$ (Limited by the resistor value chosen).
2. Non-Inverting Amplifier:
   • Voltage at inverting node by divider: $V_- = V_{\text{out}} \left(\frac{R_{\text{in}}}{R_{\text{in}} + R_f}\right) = V_+ = V_{\text{in}}$
   • Closed-Loop Gain: $A_v = \frac{V_{\text{out}}}{V_{\text{in}}} = 1 + \frac{R_f}{R_{\text{in}}}$
   • Input Impedance: $Z_{\text{in}} \approx 10^{12},\Omega$ (Near infinite; does not load signal source).
3. Voltage Follower / Unity-Gain Buffer:
   • Special non-inverting case where $R_f = 0,\Omega$ and $R_{\text{in}} = \infty$:
   • $A_v = +1.00 \implies V_{\text{out}} = V_{\text{in}}$
   • Utilized between patient skin electrodes and subsequent active filters to prevent electrode impedance loading.
4. Summing Amplifier (Inverting): $V_{\text{out}} = -R_f \left(\frac{V_1}{R_1} + \frac{V_2}{R_2} + \frac{V_3}{R_3} + \dots\right)$
5. Standard Difference Amplifier:
   • When matched resistors are used ($R_1 = R_3$ and $R_2 = R_4$): $V_{\text{out}} = \frac{R_2}{R_1} (V_2 - V_1)$
   • Major Limitation for Bioamplifiers: The input impedance of the inverting input is relatively low ($Z_{\text{in}} = R_1$). Any slight imbalance in patient electrode-skin contact impedance degrades common-mode rejection drastically.

---

3. The Three-Op-Amp Instrumentation Amplifier (INA)

To overcome the input impedance limitations of simple difference amplifiers, biomedical monitoring systems utilize the Three-Op-Amp Instrumentation Amplifier (INA) (e.g., AD620, INA118, INA128).

+-----------------------------------------------------------------------------+
|                   THREE-OP-AMP INSTRUMENTATION AMPLIFIER (INA)              |
|                                                                             |
|   (+) Lead o-----+                                                          |
|   (e.g., LA)     |                                                          |
|                +-v-+                                                        |
|                |A1 |---------------------\                                  |
|                +---+                      \                                 |
|                  |                          \                               |
|                 [R1]                     [R2: 10k]                          |
|                  |                           |                              |
|                  *---[ Rg (Gain Set) ]---*   +-------(-)                    |
|                  |                       |           \                      |
|                 [R1]                     |            >--+----o Vout        |
|                  |                       |   +-------(+)    (To Filter/ADC) |
|                +-v-+                     |   |                              |
|                |A2 |---------------------+   |                              |
|                +---+                     [R3: 10k]                          |
|   (-) Lead o-----+                           |                              |
|   (e.g., RA)                                [R4: 10k]                       |
|                                              |                              |
|                                             GND                             |
|                                                                             |
|   STAGE 1: Dual Non-Inverting Buffers        STAGE 2: Difference Amplifier  |
+-----------------------------------------------------------------------------+

Mathematical Derivation of INA Gain:

1. Stage 1 consists of op-amps A1 and A2 acting as non-inverting buffers for common-mode signals, but providing differential amplification across gain-setting resistor $R_g$.
2. The differential output voltage between the outputs of A1 and A2 is: $V_{o1} - V_{o2} = \left(1 + \frac{2 R_1}{R_g}\right) (V_{\text{in}+} - V_{\text{in}-})$
3. Stage 2 is a unity-gain difference amplifier with laser-trimmed resistors ($R_2 = R_3 = R_4 = 10\text{ k}\Omega$): $V_{\text{out}} = \frac{R_4}{R_2} (V_{o1} - V_{o2}) = 1 \cdot (V_{o1} - V_{o2})$
4. Overall INA Voltage Gain Formula: $G = \frac{V_{\text{out}}}{V_{\text{in}+} - V_{\text{in}-}} = 1 + \frac{2 R_1}{R_g}$

Key Advantages of the Instrumentation Amplifier in Medical Devices:

• Ultra-High Input Impedance ($Z_{\text{in}} > 10^{10},\Omega = 10\text{ G}\Omega$): Because both differential inputs connect directly to non-inverting op-amp gates, the amplifier draws zero current from delicate patient bioelectrodes.
• Single External Gain Resistor ($R_g$): System gain can be dialed from $1$ to $>1,000$ by changing a single precision resistor without altering circuit symmetry.
• Outstanding Common Mode Rejection Ratio (CMRR $> 100\text{ dB}$ to $120\text{ dB}$).

---

4. Common Mode Rejection Ratio (CMRR) & Right Leg Drive (RLD)

+-----------------------------------------------------------------------------+
|                  COMMON-MODE NOISE VS. DIFFERENTIAL ECG SIGNAL              |
|                                                                             |
|   60 Hz Mains Electric Field                                                |
|   ~~~~~~~~~~> Couples Capacitively into Patient Body                        |
|                                                                             |
|   Lead LA:  V_LA = V_Common (1.0 V @ 60Hz) + 0.5 * V_ECG (0.5 mV)           |
|   Lead RA:  V_RA = V_Common (1.0 V @ 60Hz) - 0.5 * V_ECG (0.5 mV)           |
|                                                                             |
|   Differential Signal (V_diff) = V_LA - V_RA = 1.0 mV (Pure ECG)            |
|   Common-Mode Noise (V_cm)     = (V_LA + V_RA) / 2 = 1.0 V (1000x larger!)  |
+-----------------------------------------------------------------------------+

CMRR Mathematical Definition:

$\text{CMRR} = \frac{|A_d|}{|A_{cm}|}$

$\text{CMRR}_{\text{dB}} = 20 \cdot \log_{10}\left(\frac{A_d}{A_{cm}}\right)$

Where:

• $A_d = \text{Differential Gain} = \frac{\Delta V_{\text{out}}}{\Delta(V_+ - V_-)}$
• $A_{cm} = \text{Common-Mode Gain} = \frac{\Delta V_{\text{out}}}{\Delta V_{cm}}$

[!NOTE] CMRR Practical Example: An ECG preamplifier has a differential gain $A_d = 1,000$ ($60\text{ dB}$) and a CMRR of $100\text{ dB}$ ($100,000:1$).

1. Solve for Common-Mode Gain: $100\text{ dB} = 20 \log_{10}\left(\frac{1000}{A_{cm}}\right) \implies 5 = \log_{10}\left(\frac{1000}{A_{cm}}\right) \implies \frac{1000}{A_{cm}} = 10^5 \implies A_{cm} = 0.01$.
2. If a $1.0\text{ V}{\text{RMS}}$ common-mode $60\text{ Hz}$ noise is induced on the patient, the output noise is $V{\text{out(noise)}} = 1.0\text{ V} \times 0.01 = 0.01\text{ V} = 10\text{ mV}$.
3. The patient's $1.0\text{ mV}$ ECG signal is amplified to $V_{\text{out(ECG)}} = 1.0\text{ mV} \times 1000 = 1000\text{ mV} = 1.0\text{ V}$.
4. Signal-to-Noise Ratio at Output: $\frac{1000\text{ mV}}{10\text{ mV}} = 100:1$, cleanly preserving the ECG waveform!

The Right Leg Drive (RLD) Circuit

To further suppress common-mode powerline noise, biomedical patient monitors use a Right Leg Drive (RLD) active feedback circuit:

1. The common-mode voltage present on the patient's limbs is sensed by averaging the potential at the Wilson Central Terminal or the output of the first INA stage.
2. An auxiliary inverting amplifier inverts the common-mode noise ($180^\circ$ phase shift), amplifies it, and drives it back to the patient's Right Leg (RL) electrode through a current-limiting safety resistor ($39\text{ k}\Omega$ to $100\text{ k}\Omega$).
3. This active cancellation dynamically forces the patient's body potential to virtual ground, reducing common-mode interference by an additional $20\text{ dB to }40\text{ dB}$.

---

5. Active Filter Topologies for Biomedical Signal Processing

Biomedical bio-signals occupy distinct physiological frequency bands:

• Diagnostic ECG Bandwidth: $0.05\text{ Hz to }150\text{ Hz}$ (AAMI/AHA standard to accurately render ST-segment elevation/depression and pediatric QRS spikes).
• Monitoring ECG Bandwidth: $0.5\text{ Hz to }40\text{ Hz}$ (Reduces motion artifact and respiratory baseline wander).
• EEG Bandwidth: $0.5\text{ Hz to }70\text{ Hz}$ (Delta, Theta, Alpha, Beta, Gamma rhythms).
• EMG Bandwidth: $10\text{ Hz to }500\text{ Hz}$.

+-----------------------------------------------------------------------------+
|                        ACTIVE FILTER TOPOLOGIES                             |
|                                                                             |
|   [2ND-ORDER SALLEN-KEY LOW-PASS]        [ACTIVE TWIN-T 60Hz NOTCH FILTER]  |
|               C1                                  C       C                 |
|         +-----||-----+                     +-----||---*---||-----+          |
|         |            |                     |          |          |          |
|   Vin -/\/\/---*--/\/\/--(+)         Vin -*---/\/\/---*--/\/\/---*--(+)     |
|        R1      |   R2    \                 |   R      |   R      |   \  |
|               ---         >-- Vout         |         ---         |    >-+
|            C2 ---     +--(-)               |      2C ---         |   /  |
|                |      |                    |          |          +--(-) |
|               GND     +--+                 |         GND         |  |   |
|                          |                 +----------*----------+  |   |
|                          +----------------------------+             |   |
|   fc = 1 / ( 2*pi*R*C )                               R/2           |   |
|   Roll-off = -40 dB/decade                 f0 = 1 / ( 2*pi*R*C )    |   |
+-----------------------------------------------------------------------------+

Key Active Filter Configurations:

1. Sallen-Key Second-Order Low-Pass Filter: Uses an op-amp with two resistors and two capacitors to create a 2-pole low-pass response with a steep $-40\text{ dB/decade}$ ($-12\text{ dB/octave}$) roll-off: $f_c = \frac{1}{2\pi \sqrt{R_1 R_2 C_1 C_2}}$ $\text{When } R_1 = R_2 = R \text{ and } C_1 = C_2 = C: \quad f_c = \frac{1}{2\pi R C}$
2. Sallen-Key High-Pass Filter: Swaps resistor and capacitor locations. Eliminates the DC half-cell polarization offset ($100\text{ to }300\text{ mV}_{\text{DC}}$) generated chemically at the $\text{Ag/AgCl}$ electrode-electrolyte skin interface ($f_c = 0.05\text{ Hz}$ for diagnostic ECG).
3. Active Twin-T Notch Filter: A dual-T RC network providing extreme attenuation (notch depth $>40\text{ dB}$) at the specific powerline frequency ($60\text{ Hz}$ in North America, $50\text{ Hz}$ in Europe): $f_0 = \frac{1}{2\pi R C}$ Where the upper T consists of two series resistors $R$ and a shunt capacitor $2C$, and the lower T consists of two series capacitors $C$ and a shunt resistor $R/2$.