IEEE Solid-State Circuits Magazine - Spring 2016 - 8

SOS (f)
Sin(f)
f

(a)
PSD of Chopped vin(t )

SOS (f)

(b)

f

LPf
PSD of Chopped VOS

f0

2f0
(c)

3f0

f

FigURe 2: The PSD of signals in the chopper amplifier. (a) Both the input signal and the offset
voltage occupy the same frequency band around dc. (b) After the first chopping operation,
the signal spectrum is shifted to odd multiples of f0 while the offset voltage remains centered
around dc. (c) At the output node, the signal spectrum is down-converted to around dc while
the offset voltage is shifted up in frequency. A low-pass filter can easily separate the two.

ϕ1
+
Vin
-

ϕ1
VOS

ϕ2

ϕ2

+

- +

A

ϕ2

-

ϕ1

Vout
-

ϕ1

Amplifier
with Offset

Chopper

+

ϕ2

Chopper

(a)
During ϕ2

During ϕ1
VOS
+
Vin
-

- +

VOS

+
A
-

+ +
Vout Vin
- -

- +

+
A
-

+
Vout
-

(b)
FigURe 3: A differential implementation of chopper amplifier. (a) Multiplication by +1 is
achieved during {1 and by -1 during {2 and (b) equivalent chopper amplifier circuit during {1 and {2 .

Since p 2 (t) = 1, we can write
v out (t) = A (v in (t) + VOS p (t)) .
Note that the output voltage Vout (t)
is the sum of two signals: the input
waveform and the chopped offset
voltage, both amplified by A.
To see how we can separate the
desired output signal (Av in (t)) from

8

s p r i n g 2 0 16

the undesired output signal (AVos p (t)),
let us examine these signals in the frequency domain.
Figure 2(a) shows the power spectral density (PSD) of the input signal
S in (f) in black and the PSD of the
offset voltage S OS (f ) in red. Even
though the offset voltage is considered a dc quantity, we have assumed
an offset that may vary slowly with

IEEE SOLID-STATE CIRCUITS MAGAZINE

time and, hence, considered a nonzero bandwidth for the offset. This
also includes the effect of flicker
noise, a type of low-frequency noise
whose PSD exhibits 1/f behavior. In
this case, Vin (t) and Vos overlap in
their frequency content as shown
and need to be separated.
The first chopping operation can
be considered as an up-conversion
(modulation) of the input signal to
odd multiples of f0, where f0 is the
fundamental frequency of p (t) . This
is because p (t) , which is a square
wave, is an odd function of time and,
when expanded into its Fourier series,
will only have components at odd
multiples of f0 . Therefore, as shown
in Figure 2(b), the up-conversion creates scaled copies of the spectrum
centered around odd multiples of f0,
with the scaling factors being the Fourier coefficients of p (t) .
Upon a second chopping operation, the scaled up-converted copies
of the input spectrum will all add up
at around dc to reproduce the original input spectrum as shown in Figure 2(c). However, the offset voltage
now experiences an up-conversion,
and hence its frequency content will
be shifted to around odd multiples of
f0 , with no frequency content around
dc. If f0 is chosen to be sufficiently
larger than the sum of the signal
bandwidth and the offset bandwidth
(actually, the flicker noise corner frequency), one can see that the chopper
amplifier fully separates the signal
from the chopped offset voltage. A
simple low-pass filter can then easily
preserve the input signal but eliminate the chopped offset voltage (and
flicker noise).
Now let us see how we can implement a chopper amplifier. The multiplication by p (t) is really simple if
we opt for a fully differential implementation. As shown in Figure 3,
the multiplication by -1 is simply
implemented by swapping the two
wires whereas the multiplication by
one is implemented by not swapping
the wires. In this figure, the multiplication by one is accomplished during
phase 1 of the clock ( { 1: red switches)
whereas the multiplication by -1 is
Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Spring 2016
