IEEE Solid-States Circuits Magazine - Fall 2022 - 13

to disturb it. The self-correcting action
of feedback makes loop nodes
look like they have low impedance.
However, as the loop gain drops, the
impedance rises, making the nodes
vulnerable to any source of coupling.
With Bandini Mountain choking off
the supply, 100 MHz is going to be the
noisiest frequency, but your feedback
circuit is probably not going to be able
to suppress it. For 60 dB of loop gain to
be at full strength at 100 MHz, it would
need to have a unity gain frequency
of 100 GHz (assuming single-pole roll
off). That's not going to happen. In
fact, many practical circuits have already
crossed unity gain by 100 MHz,
so feedback provides no PSRR protection
against Bandini Mountain at all.
Your block cannot protect itself from
supply junk, and it cannot hold its own
output steady against coupling from
nearby wires.
Figure 3 illustrates this effect with
an example circuit. An idealized feedback
loop with 60 dB of loop gain surrounds
a vulnerable high-impedance
node, labeled " X. " This node is coupled
to VDD by a 10-fF capacitor. To simulate
the effect of PDN resonance,
a " fake noise " generator uses a tank
circuit to create a Bandini-shaped ac
signal that is superimposed on the
VDD supply.
Please note that the circuit in Figure
3 does not generate noise. It effectively
uses a swept sine wave with
an amplitude-versus-frequency profile
similar to the dreaded Bandini Mountain
so that we can see how noise might
propagate through the example loop.
Also note that you cannot reliably use
this method to verify a real-life circuit
because you cannot know the exact
Bandini frequency and shape, nor can
you accurately predict the total chip
noise that will stimulate the Bandini
tank. Figure 3 is just an illustration.
Figure 4 shows how the circuit of
Figure 3 performs over frequency.
(Cload
= 0 for Figure 4.) High loop gain
keeps the impedance of " Node X " modest
at dc. But as the loop gain declines
in single-pole fashion, the " Node X "
impedance rises at 20 dB/decade. At
the same time, the impedance of the
C parasitic
coupling capacitor is falling at
Bandini
−20 dB/decade. So, the total coupling
is increasing at 40 dB/decade, as is evident
in the PSRR. By 100 MHz, the PSRR
has dropped to 0 dB, and virtually all
the Bandini noise makes its way to the
circuit output.
Package
Inductance
On-Chip
Bypass Cap
(a)
10
I don't want to keep you awake at
night, but it gets worse. Most feedback
loops don't cross over 0 dB with
a full 90° of phase margin. It's not unusual
to have a modest amount of
peaking in the closed loop response.
VDD
Active
Circuitry
VSS
1
Amount of
ODC
0.1
1E7
1E8
Frequency (Hz)
(b)
FIGURE 2: Your power supply from 50,000 ft. (a) The basic setup. The supply rails are
usually considered to be an ac short at the board. (b) Bandini Mountain: impedance versus
frequency in Hz as seen from the on-chip circuitry. ODC: on-die capacitance. (From [1]).
VDD
Edd 1x
Vdd 3 v
Vcml
Vcml
1.5 v
R1
100 kΩ Vcml
Gain_Stage
Avol = 1,000
GBW = 100 MHz
Bandini
Rdamp L1
1.2 Ω
C1
1 nH
2.54 nF
Rwideband
0.3 Ω
Inoise
dc = 0
ac = 0.1 v
" Fake Noise " Generator
(Do Not Tweet)
Buffer_Stage
Avol = 1
Cparasitic
10 fF
1E9
ODC = 0
ODC = 100
ODC = 200
ODC = 300
ODC = 400
ODC = 500
pF
2E9
Node " X "
R2
Output
1 kΩ
GBW = 100 MHz
Cload
FIGURE 3: An example loop victim with Bandini-shaped noise on the VDD.
GBW: gain-bandwidth.
IEEE SOLID-STATE CIRCUITS MAGAZINE
FALL 2022
13
Power Supply
(ac Short)
IEEE Solid-States Circuits Magazine - Fall 2022

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