Buck-boost converter

Intent

• Compute the buck-boost’s output magnitude, inductor current and ripple at an operating point.
• Explain why its switch and diode must block the sum of input and output voltage.
• Compare its currents and stresses with those of the buck and the boost.

Theory

Circuit and conversion ratio

Inverting buck-boost converter. $L$ takes energy from $V_g$ while $Q_1$ is on and delivers it to the output through $D_1$ while $Q_1$ is off. The output is negative; $V$ is its magnitude. [Erickson & Maksimović 2020, Ch. 2]

The buck-boost converter connects the inductor to the input through the switch, and to the output through the diode. While the switch is on, the inductor stores energy from the input; while the diode conducts, it releases that energy into the output, with the polarity reversed [Erickson & Maksimović 2020, Ch. 2]. The conversion ratio is therefore negative (buck-boost conversion ratio). Working with the output magnitude:

$$V = \frac{D V_g}{1 - D}$$

$V$

output voltage

$D$

duty ratio

$V_g$

input voltage

Buck-boost output voltage magnitude, CCM✓ verified by 7 tests

Assumptions, convention and source

Assumptions

• ideal (lossless) switches and passive components
• continuous conduction mode (CCM)
• periodic steady state
• small-ripple approximation

Convention

magnitude of the inverted output; $V$ is positive

Source

Erickson & Maksimović 2020, Ch. 2 (Principles of Steady-State Converter Analysis)

Derivation

step-by-step sympy derivation

Equation id

buckboost.V · equations.yaml entry

It steps down for $D < 0.5$ and up for $D > 0.5$.

Inductor current and ripple

The input and the output are never connected to the inductor at the same time, so the inductor current reaches the output only during the off-interval. Charge balance gives the same form as in the boost:

$$I_L = \frac{V}{\left(1 - D\right) R}$$

$I_L$

dc inductor current

$D$

duty ratio

$R$

load resistance

$V$

output voltage

Buck-boost dc inductor current, CCM✓ verified by 7 tests

Assumptions, convention and source

Assumptions

• ideal (lossless) switches and passive components
• continuous conduction mode (CCM)
• periodic steady state
• small-ripple approximation
• resistive load R

Notes

the inductor delivers current to the output only during the off-interval

Source

Erickson & Maksimović 2020, Ch. 2 (Principles of Steady-State Converter Analysis)

Derivation

step-by-step sympy derivation

Equation id

buckboost.IL · equations.yaml entry

While the switch is on, the inductor sees the input voltage:

$$\Delta i_L = \frac{V_g D T_s}{2 L}$$

$\Delta i_L$

inductor ripple, half peak-to-peak

$D$

duty ratio

$L$

inductance

$T_s$

switching period

$V_g$

input voltage

Buck-boost inductor current ripple (half peak-to-peak), CCM✓ verified by 7 tests

Assumptions, convention and source

Assumptions

• ideal (lossless) switches and passive components
• continuous conduction mode (CCM)
• periodic steady state
• small-ripple approximation

Source

Erickson & Maksimović 2020, Ch. 2 (Principles of Steady-State Converter Analysis)

Derivation

step-by-step sympy derivation

Equation id

buckboost.ripple.iL · equations.yaml entry

and the switch and the diode both carry its peak (peak current).

Output voltage ripple

As in the boost, the capacitor alone supplies the load while the switch is on [Erickson & Maksimović 2020, Ch. 2]:

$$\Delta v = \frac{V D T_s}{2 R C}$$

$\Delta v$

output ripple, half peak-to-peak

$C$

capacitance (output capacitor)

$D$

duty ratio

$R$

load resistance

$T_s$

switching period

$V$

output voltage

Buck-boost output voltage ripple (half peak-to-peak), CCM✓ verified by 7 tests

Assumptions, convention and source

Assumptions

• ideal (lossless) switches and passive components
• continuous conduction mode (CCM)
• periodic steady state
• small-ripple approximation
• resistive load R

Notes

while the switch is on, the capacitor alone supplies the load

Source

Erickson & Maksimović 2020, Ch. 2 (Principles of Steady-State Converter Analysis)

Derivation

step-by-step sympy derivation

Equation id

buckboost.ripple.v · equations.yaml entry

Both its input and output currents are pulsed: the input draws current only during the on-interval, the output receives it only during the off-interval.

Switch stress

While the diode conducts, the far end of the switch sits at the (negative) output voltage, so the switch blocks the input voltage plus the output magnitude; while the switch is on, the diode blocks the same sum [Erickson & Maksimović 2020, Ch. 6]:

$$V_\mathrm{DS} = V_g + V$$

$V_\mathrm{DS}$

switch voltage while off

$V$

output voltage

$V_g$

input voltage

Buck-boost switch voltage while off (also the diode's blocking voltage)✓ verified by 7 tests

Assumptions, convention and source

Assumptions

• ideal (lossless) switches and passive components
• continuous conduction mode (CCM)
• periodic steady state
• small-ripple approximation

Source

Erickson & Maksimović 2020, Ch. 6 (Converter Circuits)

Derivation

step-by-step sympy derivation

Equation id

buckboost.Vds · equations.yaml entry

This sum exceeds both the input and the output voltage: the price of a single stage that can step up or down. The small-signal model also has a right-half-plane zero (RHP zero). The flyback converter is the transformer-isolated version of this circuit (see the flyback page).

Operating modes

This section looks at one steady period of the example, mode by mode. The waveforms come from the site’s simulator, whose operating-mode view draws the same for any values. In CCM the period has two modes: the switch conducts and the inductor charges from the input while the capacitor alone feeds the load, then the switch is off and the diode carries the inductor’s current into the output, which it charges negative [Erickson & Maksimović 2020, Ch. 2].

carries current  no current

(a) Mode 1 switch on (t₀ to t₁: 0 s to 5 µs, 5 µs)

S conducts: L is connected across the input. D blocks. The voltage across L averages 12 V. L's current grows: it stores energy. C discharges. The input delivers power.

(b) Mode 2 switch off (t₁ to t₂: 5 µs to 10 µs, 5 µs)

S is off: L's current flows on through D into the output, whose voltage is inverted. The voltage across L averages −12 V. L's current shrinks: it releases energy. C charges. The input supplies nothing.

The operating modes of one steady period of the example buckboost-basic, from the site's simulator: the key waveforms with the modes' boundaries $t_0, t_1, \ldots$, then the circuit in each mode, its current-carrying branches in colour. ▶ Change the values in the simulator

Worked example

The buck-boost example of the volt-second balance page:

Buck-boost example

Symbol	Value	How it is obtained
$V_g$ input voltage	12 V	given
$D$ duty ratio	0.5	given
$f_s$ switching frequency	100 kHz	given
$L$ inductance	100 µH	given
$C$ capacitance (output capacitor)	10 µF	given
$R$ load resistance	10 Ω	given
$V$ output voltage	12 V	Buck-boost output voltage magnitude, CCM
$I_L$ dc inductor current	2.4 A	Buck-boost dc inductor current, CCM
$\Delta i_L$ inductor ripple, half peak-to-peak	300 mA	Buck-boost inductor current ripple (half peak-to-peak), CCM
$I_\mathrm{pk}$ peak current	2.7 A	Peak inductor current: dc value plus half the ripple
$\Delta v$ output ripple, half peak-to-peak	300 mV	Buck-boost output voltage ripple (half peak-to-peak), CCM
$V_\mathrm{DS}$ switch voltage while off	24 V	Buck-boost switch voltage while off (also the diode's blocking voltage)
$K$ inductor parameter (CCM vs DCM)	2	Dimensionless inductor parameter K
$K_\mathrm{crit}$ K at the CCM/DCM boundary	0.25	Critical K of the buck-boost converter

Operating mode: CCM ($K > K_\mathrm{crit}$: holds)

At this duty ratio the output magnitude equals the input voltage, yet the switch must block 24 V and carry 2.7 A at the peak.

Try it

▶ Open in the equation explorer: Buck-boost switch voltage while off (also the diode's blocking voltage)
Preset from the example buckboost-basic

▶ Open in the simulator: Buck-boost
Preset from the example buckboost-basic

Sweep the output magnitude $V$: every volt of output adds a volt to the switch stress, on top of the input voltage.

Bench exercise

On a buck-boost (inverting) evaluation board, measure the output with the oscilloscope’s ground clip on the converter’s ground: the output is negative. Measure the switch voltage while it is off and compare it with the sum of the input voltage and the output magnitude; then observe the input current with a current probe and note that it flows in pulses.

Gotchas

• The output is inverted. A load, a measurement or a feedback divider that assumes a positive output will read or regulate the wrong polarity.
• Both terminals see pulsed current. Input and output capacitors both carry large ripple currents, unlike the buck (continuous output current) or the boost (continuous input current).
• Stress grows with both voltages. At a high step-up ratio the output magnitude dominates the switch stress; at a deep step-down the input does.

Go deeper

• Application note Understanding Inverting Buck-Boost Power Stages in Switch Mode Power Supplies (SLVA059) — E. Rogers, Texas Instruments · retrieved 2026-09-23
  The inverting buck-boost power stage analysed the same way.
• Book chapter Converter Circuits (Ch. 6) — R. W. Erickson, D. Maksimović · retrieved 2026-09-23
  How the basic topologies relate, and transformer-isolated versions including the flyback and forward converters.
• Course Converter Circuits — University of Colorado Boulder (Coursera) · retrieved 2026-09-23
  DCM analysis and the isolated converter circuits, following the same textbook.

Quiz

1. An ideal CCM buck-boost runs from $12\,\mathrm{V}$ at $D = 0.75$. What is the magnitude of its output voltage?

   1. $4\,\mathrm{V}$
   2. $9\,\mathrm{V}$
   3. $16\,\mathrm{V}$
   4. $36\,\mathrm{V}$
   Answer and explanation

   Correct answer: D The magnitude is $D V_g/(1 - D)$: three times the input voltage at this duty ratio.

2. An ideal buck-boost has a $12\,\mathrm{V}$ input and a $-24\,\mathrm{V}$ output. What voltage must its switch block while off?

   1. $12\,\mathrm{V}$
   2. $24\,\mathrm{V}$
   3. $36\,\mathrm{V}$
   4. $48\,\mathrm{V}$
   Answer and explanation

   Correct answer: C While the diode conducts, the switch sits between the input and the negative output, so it blocks the input voltage plus the output magnitude.

3. In which interval does the buck-boost inductor deliver current to the output?

   1. Only while the switch is on
   2. Only while the diode conducts
   3. In both intervals
   4. Only in DCM
   Answer and explanation

   Correct answer: B While the switch is on, the inductor is connected to the input; only when the diode conducts is it connected to the output.

4. A buck-boost delivers $12\,\mathrm{V}$ (magnitude) into $6\,\Omega$ at $D = 0.5$. What is its dc inductor current?

   1. $1\,\mathrm{A}$
   2. $2\,\mathrm{A}$
   3. $4\,\mathrm{A}$
   4. $6\,\mathrm{A}$
   Answer and explanation

   Correct answer: C The load current is $2\,\mathrm{A}$, and it is delivered only during the off-interval, so the inductor current is larger by $1/(1 - D)$.

5. Which of the three basic converters draws a pulsed current at both its input and its output?

   1. The buck
   2. The boost
   3. The buck-boost
   4. None of them
   Answer and explanation

   Correct answer: C The buck has a continuous output current and the boost a continuous input current; the buck-boost connects the inductor to the input and the output only alternately.

6. Why is the switch stress of a buck-boost higher than that of a buck or a boost at the same input and output magnitudes?

   1. Its switch carries no current
   2. Its switch blocks the sum of input voltage and output magnitude, not just one of them
   3. Its switching frequency is higher
   4. It operates only in DCM
   Answer and explanation

   Correct answer: B The buck switch blocks $V_g$ and the boost switch blocks $V$; the buck-boost switch sits between the input and the inverted output, so it blocks $V_g + V$.