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CMRR, Common Mode Rejection Ratio
CMRR is the ability of a differential amplifier with two input circuits to reject an input signal (noise component Vn) common to both inputs.
When a mains supply signal (In) flows through a ground circuit, it produces a noise signal (Vn) that is applied to the differential amplifier as a common-mode component. However, the common-mode noise component appearing at the amplifier output is very small (the common-mode gain is very low, ideally zero).
If the differential gain (the gain for Vs in the figure) is Adiff and the common-mode gain (the gain for Vn in the figure) is Acom, CMRR is defined by the following formula:
CMRR = Adiff/Acom = Adiff [dB] - Acom [dB]
For example, the PMK BumbleBEE high-voltage differential probe still achieves a CMRR of 62 dB (minimum) at 3.2 MHz.
As the system grows larger, (1) and (2) appear identical, but because their potentials and impedances differ, current flows through the ground circuit between (1) and (2) and becomes noise.
In practice, a differential amplifier requires signal lines, and the signal source has output impedance. The figure below therefore shows a simplified equivalent circuit for a differential amplifier in use. Without these impedances, the noise source would be applied at exactly the same voltage to the positive and negative input terminals of the differential amplifier, and CMRR would not degrade. In reality, however, these values cannot be ignored: when the noise source is applied to the positive and negative inputs of the differential amplifier, a voltage difference appears, and this difference degrades CMRR.
First, a simple example: signal source impedance Rs = 10 kΩ, differential amplifier Rin+ = Rin- = 10 MΩ input resistance (neglected), and other impedances such as Rc neglected:
- At DC, the differential gain is 0.9990 and the common-mode gain is 0.0009990, giving a CMRR of 20log (0.9990 / 0.0009990), i.e. 60.0 dB.
Next, with Rs = 0 kΩ and Cc1 + Cin+ = Cc2 + Cin- = 500 pF:
- At 10 kHz, the differential gain is 0.9532 and the common-mode gain is 0.2994, so CMRR drops to about 0.1 dB.
Note that if there is any imbalance in the path from the signal source to the positive input terminal of the differential amplifier, CMRR will degrade. In the case shown below, an impedance equal to Rs is inserted in the negative input to improve CMRR.
Under real operating conditions, it is difficult to balance the input section over a wide range, and difficult to achieve high CMRR above several tens of kHz.
Rs: signal source output resistance
Rc1, Rc2: DC resistance of the cable
Lc1, Lc2: signal cable inductance (1 µH/m for parallel cable, 250 nH/m for 50 Ω coaxial cable)
Cc1, Cc2: signal cable capacitance (150 pF/m for shielded cable, 100 pF/m for 50 Ω coaxial cable)
