We have analyzed so far the effect of chopper modulation on white noise and 1/f noise. In order to be able to process signals without changing the baseband information, we have to modulate signals and noise differently. The principle of chopper amplifiers is illustrated in fig.5.6. For simplicity the 1/f noise has been represented on a logarithmic scale. The input signal is multiplied with a rectangular signal m(t) with unity amplitude and 50% duty-cycle. As a result, the signal is once modulated at odd harmonics of the chopper frequency. The signal will be amplified and/or filtered, modulated back, leaving spectral contributions at even harmonics of the chopper frequency.

The amplitude of the modulation signal decreases with 1/n where n is the harmonic number. Offset and 1/f noise are modulated at odd harmonics leaving the baseband free of 1/f noise. In the ideal chopping case, the bandwidth of the amplifier should be infinity. As long as this is true, multiplying the signal twice with m(t) will reconstruct the input signal ideally. If the bandwidth of the amplifier is limited, the result is a high frequency residue centered around the even harmonics and the signal in the baseband is attenuated.

To recover the signal, the output has to be low-pass filtered as shown in fig.5.7. Given the corner frequency of the 1/f noise fcorner and the cutoff frequency of the low-pass filter at the output, BWsignal the necessary condition to have complete reduction of the flicker noise in the baseband is found from:

(5.17)

Fig.5.6: The chopper technique

Fig.5.7: The baseband spectrum

To analyze the effect of chopping on the offset of the amplifier, the offset has been represented in fig.5.6 at the input of the amplifier A. As long as the frequency response of the amplifier is flat, the output voltage Vout(f) is found from the following convolution:

(5.18)

This sequence of Dirac pulses has no DC component and the offset at the output has a theoretical value of 0V. Obviously, any temperature drift of the offset voltage is also cancelled out after chopper modulation.