The piezoelectric buzzer is about the cheapest and most frugal sound source in electronics: a ceramic disc bonded to a metal plate produces a loud alert tone on a few milliamps. Getting it to sound loud and consistent, however, depends on three things: why the disc flexes, what it looks like to the drive circuit, and which frequency and waveform drive it best. This article starts from the converse piezoelectric effect, uses the Butterworth–Van Dyke (BVD) equivalent circuit to explain resonance and anti-resonance, and then covers external drive of passive buzzers, self-oscillation with a three-terminal element, and how the housing's Helmholtz cavity shapes frequency and sound pressure.

• 2–6 kHzTypical resonance range of piezo buzzer elements
• +6 dBSPL gain when a full bridge doubles the peak-to-peak drive (linear range)
• 50%Square-wave duty cycle that maximises the fundamental

1. The converse piezoelectric effect: how a ceramic disc bends

A piezoelectric ceramic – most commonly lead zirconate titanate, PZT – is poled with a strong DC field, leaving a remanent polarisation through its thickness. By convention the poling axis is direction 3 and the in-plane axes are 1 and 2. A field E₃ applied across the thickness changes not only the thickness but also the in-plane (radial) dimensions. The two strains are described by the piezoelectric coefficients d₃₃ and d₃₁:

On its own the radial motion is tiny. As an illustration, take d₃₁ = −170 pC/N (typical of soft PZT), a 0.1 mm thick disc and 10 V: E₃ = 1 × 10⁵ V/m and S₁ = −1.7 × 10⁻⁵. The rim of a 10 mm radius disc moves only about 0.17 μm – far too little to move air.

The buzzer element solves this by bonding the ceramic to a larger brass or nickel-alloy plate, forming a unimorph. When the ceramic contracts radially the plate does not, so the mismatch forces the laminate to bend, much like a bimetallic strip when heated; reverse the voltage and it bends the other way. Bending converts a minute in-plane strain into a clearly visible out-of-plane displacement. Under AC drive the element flexes back and forth and radiates sound.

The natural frequency of the bending mode is set by materials and geometry. For a uniform thin circular plate it scales with t/D²·√(Y/ρ), where t is thickness, D diameter, Y Young's modulus and ρ density: a thicker plate resonates higher, a larger one lower. In a laminate the thickness ratio and the ceramic-to-plate diameter ratio also affect coupling and resonance. Equally important is how the element is supported. Holding it near its nodal circle – the ring where vibration displacement is zero – absorbs almost no vibration energy, giving a sharp resonance and high output. Clamping the whole rim is mechanically robust and less sensitive to assembly tolerances, but changes both the resonance and the output. That is why the same element can measure differently in different housings.

2. The BVD equivalent circuit: a capacitor plus a series resonant branch

Around resonance, a piezo element is well described by the Butterworth–Van Dyke model (Figure 2): the dielectric capacitance C₀ between the electrodes, in parallel with a motional branch of R₁, L₁ and C₁ in series. The motional branch is the mechanical system reflected to the electrical side: L₁ represents moving mass, C₁ compliance and R₁ mechanical loss plus acoustic radiation. The idea is the same as reflecting a loudspeaker's moving system into a parallel RLC, except that the piezo element couples voltage to force, so the reflected network is a series branch.

The circuit has two characteristic frequencies. Where the motional branch is series-resonant the impedance is lowest: this is the resonance frequency f_r (strictly the series resonance f_s; the two are practically equal at low loss). Slightly above f_r the motional branch turns inductive and resonates in parallel with C₀, giving maximum impedance at the anti-resonance frequency f_a:

C₀ can be estimated as a parallel-plate capacitor, C₀ ≈ ε₃₃^T·A / t. Example: a 20 mm diameter, 0.2 mm thick disc with a relative permittivity of 1800 (a common figure for soft PZT) gives C₀ ≈ 1800 × 8.854 × 10⁻¹² × 3.14 × 10⁻⁴ / 2 × 10⁻⁴ ≈ 25 nF. Element datasheets usually list this capacitance, and it is the main load the driver sees.

3. The impedance curve: where the element is loudest

Figure 3 shows the impedance magnitude of an example element calculated from the BVD model with C₀ = 20 nF, C₁ = 2 nF, f_r = 4.0 kHz and Q_m = 60, which give L₁ ≈ 0.79 H and R₁ ≈ 332 Ω.

Three things stand out:

• Away from resonance the element is simply a capacitor. The curve follows 1/(2πfC₀) closely; at 4 kHz, C₀ alone is about 2 kΩ. This governs the charge/discharge current under square-wave drive (Section 4).
• Impedance is lowest at resonance (about 323 Ω here) and vibration is strongest. At constant drive voltage the motional current – i.e. the vibration velocity – peaks near f_r, so a passive buzzer is loudest when driven close to its rated resonance. Move away and SPL falls noticeably.
• Impedance peaks at anti-resonance (about 11.1 kΩ here). In the example f_a/f_r = √1.1 ≈ 1.049, i.e. k_eff ≈ 0.30. Sweeping both frequencies on an impedance analyser therefore yields k_eff and checks poling and bonding: a poor bond, a cracked disc or depoling all blunt the resonance and pull f_a and f_r together.

4. Driving a passive buzzer: frequency, waveform and circuit

A passive (externally driven) piezo buzzer has no oscillator inside, so a microcontroller or driver IC must supply the AC signal. Three questions shape the design.

Square waves and duty cycle

A microcontroller most easily produces a square wave. A symmetric square wave of ±A contains only odd harmonics; its fundamental has amplitude (4/π)A ≈ 1.27A, and the 3rd and 5th harmonics are 1/3 and 1/5 of the fundamental. Because the element responds far more strongly near resonance than elsewhere, most harmonic content is not amplified and the tone is dominated by the fundamental. For a pulse train with duty cycle D, the fundamental is proportional to sin(πD):

Charging a capacitive load

At every edge the driver must charge or discharge C₀, and the peak current is limited only by the switch on-resistance and any series resistor. Ignoring the motional branch, each cycle draws about C₀V_pp² from the supply, so the average power is

Drive voltage and topology

In the linear range, displacement is proportional to drive voltage: doubling the peak-to-peak voltage adds 20 log 2 ≈ 6 dB of SPL, while the power above rises fourfold. When the supply rail is limited, the common topologies are:

5. Active buzzers: self-oscillation with a three-terminal element

An active (self-driven) piezo buzzer sounds as soon as DC is applied. A classic way to build one uses the three-terminal element of Figure 1: a small, electrically isolated feedback electrode F is split off the ceramic face. As the main electrode M drives the whole element, the ceramic under F deforms too and, through the direct piezoelectric effect, generates a voltage on F. The small electrode acts like the secondary of a piezoelectric transformer, returning the vibration state to the drive circuit as an electrical signal.

1. Start-up

   DC is applied to a driver of one transistor and a few resistors; a small disturbance reaches electrode M through the circuit.

2. Frequency selection

   The element only responds strongly near its resonance, so the signal induced on F is concentrated around that frequency and carries a phase shift related to the vibration.

3. Sustained positive feedback

   The feedback signal drives the transistor base; near resonance the phase and gain conditions for oscillation are met and the amplitude grows until it is limited by the supply and transistor saturation.

4. Automatic tracking

   Because the element itself sets the oscillation frequency, drift in its resonance caused by temperature, ageing or mounting stress is followed automatically, keeping operation near the loudest point.

Structurally the circuit resembles a Hartley oscillator, with the piezo element serving as both the resonator and the feedback network. Its strengths are a minimal circuit that needs only an enable signal and inherent operation at resonance; its limitation is a fixed tone with no way to play different pitches. Another family of active buzzers uses a separate oscillator IC whose frequency is fixed by the chip; their output then depends on how well that frequency matches the element and housing resonance.

6. The housing as a Helmholtz resonator

The two faces of a bare element radiate in antiphase and largely cancel at low frequencies, so output is modest. A buzzer housing mounts the element over a small cavity that opens to the outside through a sound hole, forming a Helmholtz resonator: the air plug in the hole is the mass and the air in the cavity is the spring.

Example: with a hole radius a = 1 mm in a 0.5 mm wall, L′ ≈ 0.5 + 1.7 × 1 = 2.2 mm. A 0.27 cm³ front cavity gives f_H ≈ 3.97 kHz, essentially on top of the example element's resonance in Figure 3. Shrinking the cavity to 0.20 cm³ raises f_H to about 4.6 kHz; enlarging it to 0.40 cm³ lowers it to about 3.3 kHz. Since f_H scales with √(1/V), a 10% volume change shifts the resonance by roughly 5%.

Designers normally place the cavity resonance close to the element resonance so that the two reinforce each other and output at the target frequency rises sharply – one reason finished buzzers are specified at a single rated frequency. Conversely, if the end product puts another panel with its own hole in front of the buzzer, it effectively changes L′ and the volume, which can pull the resonance off and reduce output. Once the enclosure design is frozen, re-measure response or SPL in the real housing and adjust the drive frequency if needed.

7. Selection and application notes

During assembly, keep the sound hole clear of adhesive and labels, and do not let enclosure parts press on the buzzer – extra mechanical stress changes the support conditions. Where waterproofing is required, pair the buzzer with a breathable waterproof membrane and accept some loss of output and a shift in frequency.