Keithley _25232870_Stabilizing_AN Datasheet

LC´, CC´, RC´/ft.

RC´ LC´

CC´

Power Supply

Source Leads (twisted pair)

Phone

Test Fixture

Mobile Phone

L, C, R

Parasitic

Fixture
L, C, R

R

cable

L

cable

V

senseVout

ERR AMP

230X

C

cable

C

DUT, fixture

+

–

Sense

OUT

AMP

Number 2870

Application Note

Series

Stabilizing Fast Transient Response
Power Supply/Load Circuits

Introduction

Keithley’s Series 2300 Battery/Charger Simulators (fast transient
response power supplies) are specifically designed for powering
RFIC power amplifiers, mobile phone handsets, and other por­table, battery-operated products in R&D and manufacturing envi­ronments. These battery-simulating power supplies are designed
to recover very quickly from short-duration pulse load current
changes as large as 1000% (i.e., a 10× increase in load current)
and to measure the peak of the load current pulse. In order to
maintain the output voltage at the programmed output level
despite near instantaneous pulse load changes and to capture
information on pulses as short as 600µs, the power supply must
combine a fast voltage recovery time with minimal voltage droop
from the transient perturbation caused by the fast load current
change. Power supplies like the Series 2300 battery/charger
simulators must have a fast-responding, wide-bandwidth (beyond
200kHz and up to 2MHz) output stage. While this wide-band­width supply recovers quickly from large load current changes,
the wide-bandwidth output stage is much more susceptible to
the impedance of the external load circuit than conventional nar­row-bandwidth DC power supplies. Certain high reactance load
conditions, such as long wire runs and capacitive loads with low
equivalent series resistance (ESR), can cause the power supply
output to begin oscillating. This paper will describe the various
load circuit conditions that can cause oscillation and provide
methods for stabilizing the load circuit.

The DC Power Supply/
Load Circuit Combination

Figure 1. Typical connec tions between a power supply and a DUT. The power

supply is using remote-sense feedback.

Figure 1

supply is energizing a device under test (DUT), in this case, a

illustrates a typical load power circuit in which a power

mobile phone in a test fixture. The power supply is using a four­wire connection scheme consisting of a pair of power sourcing

wires and a pair of load voltage sensing wires. The wires in each
pair are twisted together to minimize spurious voltages result­ing from induced magnetic fields. The test fixtures often employ
bypass capacitors to minimize AC noise. To understand how the
load circuit performs for analysis of short load current pulses
(effectively an AC signal), the two pair of wires must be modeled
as an AC network of distributed resistive, series inductive, and
parallel capacitive components. The test fixture and DUT must
be modeled as an AC network as well. The cable capacitance, the
parallel capacitance between the wires, is usually much smaller
than the bypass capacitors added around the DUT, which are
typically on the order of 10µF or larger.

Stability Analysis of the Power
Supply/Load Circuit Combination

Figure 2. Simplified Series 2300 measurement schematic with reactive load

To analyze the Series 2300 power supply/load circuit combina­tion, the overall power supply is modeled as a feedback network
consisting of an ideal error-correcting amplifier, an ideal out­put amplifier stage, and an ideal feedback sense amplifier (see

Figure 2

the load to force the power supply output to increase its voltage
to overcome the losses in the test leads and fixture to ensure
the desired (or programmed) voltage is applied to the load. The
cables and test fixture connections/DUT are modeled as lumped­element components with the DUT and test fixture as defined by
the dominant component, the parallel capacitance of the DUT.

plot, which shows the gain and phase performance as a function
of frequency.
mance of a Model 2306 power supply into an open circuit—effec­tively, a well-behaved resistive load. The loop gain falls to 0dB
(unity gain) at a frequency slightly greater than 1MHz. If the
loop gain is equal to one, and the output phase is 0º (positive
feedback), the output will be unstable (consult the references in
notes 1 and 3 and any electronics text that discusses the theory

and remote-sense feedback

). The sense amplifier measures the voltage directly at

A feedback network’s performance is characterized by a Bode

Figure 3

shows the loop gain and phase perfor-

of feedback circuit design for more information). In the case of

totalcable

res

CL

f

2π

1

=

Cable

cableres

R

L

Qω=

=

=

TotalCableres

CR

ω

1

Total

Cable

Cable

C

L

R

1

60

40

20

0

–20

–40

–60

1kHz 10kHz 100kHz 1MHz 10MHz 100MHz

180°

100°

0°

–100°

–180°

Phase

Gain, dB

Phase

Gain

Phase
margin at
Unity Gain

Frequency

phase@Unity Gai

n

Unity Ga

in

p

oi

n

t

230X

Sen+, Src+

Sen–, Src–

C

bypass

the open circuit load, the Model 2306 has a phase margin of
about 90º above 0º, which ensures the output is stable. Circuit
design rules recommend a phase margin greater than 45º to
guarantee circuit stability under all conditions.

The actual power supply/R-L-C load circuit combination has
a multi-pole transfer function with the bandwidth and the unity
gain point determined by the power supply control loop and
the parameters of the R-L-C load. The L-C load components also
determine the resonant frequency, which is near the frequency of
oscillation. The resonant frequency (fres) is defined as follows:

If the phase margin is near 0º at this frequency, the power
supply output will oscillate. Similarly, at the resonant frequency,
the pole Q factor is:

To maximize the transient response and ensure stability, fres
needs to be greater than the bandwidth of the power supply out­put circuit, and Q needs to be as small as possible.

The following sections describe methods to ensure a stable
load circuit by effectively extending fres beyond the bandwidth
of the power supply and to minimize Q. The four methods are:

1. Decreasing L

: Using good wiring techniques and low

cable

impedance cable

2. Decreasing C

: Eliminating unnecessary capacitors, typi-

Total

cally on the test fixture

3. Increasing R

: Adding resistance to the load circuit

Cable

4. Adding a compensation network to the load circuit.

Compensating for Inadequate
Power Supply Transient Response
with a Large Load Capacitor

When large capacitors are placed in parallel with the

DUT, the capacitance does improve stability, but there are

significant performance trade-offs involved. Prior to the avail-

ability of fast transient power supplies like the Series 2300,

manufacturers of portable devices such as mobile phones had

to work with conventional power supplies, which do not have

the bandwidth to respond effectively to large, near-instan-

taneous load current changes. The solution to maintaining

a near-constant output voltage was to put a large capacitor

in parallel with the load, essentially to add a second voltage

source in the load circuit (see

values of 100µF to 4700µF typically have a large equivalent

series resistance (ESR) that reduces the Q of the load circuit.

Furthermore, the equivalent series resistance of the capacitor

increases at higher frequencies and effectively adds additional

resistance to the circuit. The increased resistance at high fre-

quencies also acts to reduce Q and greatly enhance circuit sta-

bility. However, there are two disadvantages of using a large

capacitor at the load:

1. The power supply current readback circuit can no lon-

ger be used to measure a pulse load current because

the capacitor is supplying current to the load to hold

the voltage at the load steady.

Figure 4

). Large capacitors with

Figure 3. Model 2306 battery channel/2302 closed-loop gain and phase with

Using Good Wiring Techniques
and Low Impedance Cable

Good wiring techniques minimize the coupling of external
noise into a circuit and should be used in all applications. These
techniques are essential for controlling instability in wide-band-

no load

2. Large electrolytic and tantalum capacitors have large

leakage currents, which prevents the power supply cur-

rent readback circuit from reading sleep mode or off-

state currents accurately.

Although adding a large capacitor at the load can increase

system stability, it is not a desirable solution. Using a fast tran-

sient power supply and removing the capacitor at the DUT

provides the best overall circuit performance.

Figure 4. The impact of a large bypass capacitor at the load when the DUT

load current increases.

width power supply/load circuits. Twisted-pair source and sense

R

cable

R

add

R

add

L

cable

DC

230X

C

cable

C

DUT, fixture

+

–

RcCc

f

network

< f

res

π

2

1

=

leads should be used to reduce unwanted coupling from nearby
interference sources and offer immunity to both electric and
magnetic fields. Twisting the conductor pair between source
and load minimizes the loop area, which limits the magnitude
of induced voltages and cancels these noise voltages because
they are of equal magnitude and opposite polarity in adjacent
twists. Consequently, twisted wire pairs provide better immunity
to magnetic fields than two closely spaced parallel conductors.
Moreover, twisted wire pairs reduce the emission of magnetic
fields. The current flow in the two close proximity wires is equal
and opposite, so the resulting magnetic fields effectively cancel
each other within a few inches of the pair. The twisted wire pair
has lower inductance than an untwisted pair of wires of equal
length. Typically, the inductance of a 15-foot-long (4.6m) twisted­pair cable is 2–4µH.

To minimize inductance in a given length of twisted-pair
wire, use wire with thin Teflon® insulation. Thin insulation
minimizes the loop area of the twists; and, Teflon is an insulator
with a low dielectric constant, which provides the added benefit
of minimizing the cable’s capacitance and reduces total cable
impedance.

Adding Resistance to the Load Circuit

Increasing the resistance in the load circuit reduces Q and can
enhance stability.
the addition of two resistors to the load circuit. A recommended
maximum value is 1Ω for each resistor. Using the least resistance
necessary to achieve stability is optimal; thus, if 1Ω stabilizes the
load circuit, experiment with lesser-value resistors to find the
smallest acceptable value. A small additional voltage drop in each
source lead can be overcome by the sense detection feedback
network and the error correction circuitry that ensures the volt­age at the load is maintained at the programmed value. Another
way to increase the load circuit resistance is to use thinner gauge
wire. Either method for increasing R adds damping to the circuit.
Therefore, although added resistance can improve stability, it
also increases the load circuit time constant and the power sup­ply settling time.

Figure 5

shows the recommended location for

Another way to lower cable inductance is to keep the cable
as short as possible. The closer the fixture/DUT is to the power
supply, the lower the total cable inductance. Obviously, there are
physical limitations on how close the DUT can be to the power
supply, but routing the cabling as directly as possible to keep the
cable length as short as possible helps ensure system stability.

If using twisted-pair wire and the shortest possible cables is
not sufficient to ensure stability, low inductance cables can be
used. Keithley’s Model SC-182 low inductance coaxial cable with
Teflon insulation has a 10Ω characteristic impedance. A 4.6m
length of this cable has 150–250nH of inductance. When com­pared with standard twisted cable, this is a reduction in induc­tance of an order of magnitude.

Using Teflon®-insulated twisted-pair wires, minimizing wire
length, and using the SC-182 low inductance cable help reduce
L

and enhance load circuit stability. However, using these

Cable

solutions does not alter the performance of the power supply/
load circuit combination.

Decreasing the Capacitance in the
Load Circuit

Figure 5. Adding two resistors to Series 2300 source leads to improve

stability.

Adding a Compensation Network
to the Load Circuit

A third method for improving stability involves adding two R-C
compensation networks near the power supply between cor­responding sense leads and source leads (see
technique bypasses the cable inductance and load capacitance
of the feedback network for frequencies higher than the circuit
resonant frequency (f

). The compensation capacitors (Cc) act

res

as a low impedance path for the high frequency components of
the voltage waveform as it changes due to the load current tran­sitions. Compensating capacitors effectively close the feedback
loop of the power supply/load circuit combination at approxi­mately fres and stabilize the circuit.

To compensate the power supply/load circuit combination
with this network, the 3dB point of the low pass compensation
network filter must be less than f

. Thus,

res

Figure 6

). This

Wherever possible, eliminate any capacitors in parallel with the
DUT. The Series 2300 power supplies have the wide bandwidth
and resulting fast transient response needed to maintain the
voltage at the DUT during state transitions without the help of a
parallel capacitor at the DUT. Eliminating capacitors reduces the
total capacitance in the load circuit, so removing a parallel capac­itor at the DUT will improve the load circuit’s performance.

A recommended staring point is to set Rc to 100Ω, then
determine an appropriate value of Cc to stop oscillation. Given
that the sense feedback amplifier draws very little current,
the 100Ω resistors create minimal error in the voltage at the
DUT. While this is an effective method for improving stability,

C

C

R

C

R

cable

L

cable

Sense –

R

C

Sense +

Source +

DC

230X

Source –

C

C

C

cable

C

DUT, fixture

+

–

Figure 6. Adding two compensation net works

this method reduces the effective bandwidth and the transient
response of the power supply/load circuit network.

In addition to the external compensation network, the Model
2302 and Model 2306 power supplies offer internal bandwidth
control to improve load circuit stability. The HIGH bandwidth
setting produces the fastest transient response with dynamic
loads. The LOW bandwidth setting (default instrument state) will
have a slower response but will be more stable for most loads.
The LOW bandwidth setting internally implements the compen-

sation capacitance technique shown in

Figure 6

.

Actual Instability Problem and
the Stabilizing Solution

Figure 7

curve) to a 1A load current pulse. The load is resistive and cable
length is negligible (the load is connected directly at the power
supply output terminals). The voltage at the load exhibits a 10mV
droop and 10mV overshoot in response to the rising edge and
falling edge of the load current pulse. This is as close to the ideal
response as can possibly be achieved.

depicts the actual system voltage response (lower

power supply/load circuit combination will be unstable and the
voltage at the load will oscillate as shown in

Load
Current

0.5A/Div

Load
Voltage
10mV/Div

Time 0.1ms/Div

Figure 8. System instability (Lcable =1µH , C

DUT

= 2µF)

Figure 8

.

In this case, replacing the power supply load wire pair with
the Keithley Model SC-182 Low Inductance Cable reduces the
load impedance sufficiently to stabilize the circuit.

Figure 9

shows the resulting response to the load current pulse.

Load
Current

0.5A/Div

Load
Current

0.4A/Div

Load
Voltage AC
Response
10mV/Div

Time 0.1ms/Div

Figure 7. Transient response with resistive load and negligible cable length.

A more realistic situation involves cable lengths between the
power supply and the DUT that can range from hundreds of
nanohenrys to several microhenrys. In addition, the capacitance
on the fixture and the DUT input capacitance can be as high as
tens of microfarads. At these impedance levels, the system can
be unstable. For example, with L

cable

=1µH and C

DUT

Load
Voltage
10mV/Div

Time 0.1ms/Div

Figure 9. System stabilized (122cm. SC-182 cable, C = 2µF)

= 2µF, the

Suggested Solution Sequence for Stabilizing
the Power Supply/Load Circuit Combination

Following this suggested order of steps can help solve power
supply/load circuit stability problems:

Eliminate any capacitors on the test fixture and across the

1.
DUT wherever possible.

Reduce the inductance of the power supply wiring by using

2.
wiring with Teflon insulation where possible. Alternatively,
use the SC-182 coaxial cable with Teflon insulation. Use
good wiring techniques and minimize the length of the
wiring to the DUT.

If using either a Model 2302 or a Model 2306, try switching

3.
to the LOW bandwidth setting to activate the internal com­pensation network.

If an oscillation is occurring at a frequency lower than

4.
100kHz (when using the Model 2303) or lower than
500kHz (when using the Model 2306), then try using an
external compensation network.

If an oscillation is occurring at a frequency higher than

5.
100kHz (when using the Model 2303) or higher than
500kHz (when using the Model 2306), try adding resis­tance to the power supply/load circuit. Start with 1Ω in
each source wire. If the 1Ω resistor stabilizes the circuit,
experiment with smaller values until the circuit becomes
unstable again, then choose a slightly larger value that re­stabilizes the circuit. The objective is to minimize the level
of additional resistance in the circuit to optimize transient
response. Remember that using a thinner gauge lead wire
could add sufficient resistance to accomplish the same goal
as adding resistors to the circuit.

The order of these steps is such that the initial steps have
the least impact on circuit performance. Any of the techniques
can be used in conjunction with others to resolve more difficult
power supply/load circuit combinations.

Summary

While fast transient response power supplies provide the nec­essary performance to quickly recover from large pulse load
currents, the wide bandwidth of these supplies makes them
susceptible to instability in high reactance load circuits. The load
circuit reactance is a function of the type of lead wire used, the
length of the wire leads, components on the fixture, and the
input reactance of the DUT. The combined reactance of these
circuit elements must be minimized to obtain the full perfor­mance of the fast transient power supply. Methods to reduce the
reactance include reducing cable inductance by minimizing the
length of the cable or, for best results, using the Model SC-182
low inductance cable. Increasing the load circuit resistance is
a second technique to improve stability. Using a thinner gauge
cable or adding a small resistor in each source line accomplishes
the objective of increasing the resistance in the load circuit.
Eliminating unnecessary fixture capacitors reduces total circuit
reactance and is the third technique. The fourth technique for
improving stability involves adding a compensation network to
the circuit to reduce the effective bandwidth of the circuit. Used
individually or together, these four techniques can ensure power
supply/load circuit stability and provide both a voltage output
with minimal variation during dynamic load changes and mea­surements of DC and pulse load currents. The advantages of fast
transient response power supplies far outweigh the additional
effort in load circuit configuration to ensure stable performance.

Endnotes

1. Keithley Instruments W hite Paper, Optimizing Test Performance Of Digital
Cellular Products With Ultra-High Speed Power Supplies, 2001, available at

ww w.keithley.com/data?asset=4643, retrieved July 26, 2007.

2. Campbell Scientific, Inc. White Paper, Preventing and Attacking Measurement
Noise Problems, 2001, available at ww w.campbellsci.com/documents/

whitepapers/mnoise.pdf, retrieved July 26, 2007.

3. Spectrum Software, Plotting Loop Gain And Phase Margin, available at

http://www.spectrum-soft.com/news/winter2001/loopgain.shtm, 2001,

retrieved July 26, 2007.

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Specifica tions are subject to change without no tice.

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