Design Blog / Frequency multiplication

BL-101 | Rev –

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Frequency tripling generates the desired third harmonic along with unwanted frequency components. In the FM300, two filters work at different points in the circuit to select the desired signal and reduce unwanted frequency components.

John Esterline · Esterline Research & Design

A frequency tripler uses a nonlinear circuit to produce harmonics of an applied signal. A filter then selects the third harmonic, giving an output frequency three times the input frequency. If the desired component has already been selected, why does the FM300 include another filter after its output amplifier?

The answer follows from what happens in the amplifier. Its purpose is to provide the drive needed by the output network and the receiving circuit. In doing so, it can change the shape of the waveform and introduce additional harmonics. The interstage filter acts on the limiter’s output; the output filter acts on the amplifier’s output. Placing filters at both locations allows frequency selection and output drive to be developed together. [1, pp. 3–4]

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Selecting the third harmonic

The FM300 input network couples the source into the limiting stage and establishes its input loading and DC bias. As the applied waveform crosses the switching thresholds, the limiter produces a switching waveform. An ideal symmetric waveform with equal high and low times contains the fundamental and odd harmonics. The third harmonic is already present in this waveform, along with components that are unwanted at the tripler output. [1, p. 2]

The interstage band-pass filter passes the region around the third harmonic and attenuates the other, separated components. For the illustrated 20 MHz input, the desired component is at 60 MHz. The original 20 MHz component and higher limiter harmonics are unwanted at this point. Figure 3 shows how frequency selection changes their relative amplitudes.

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A filter transmits each frequency according to its response at that frequency. It does not identify a component by its harmonic order. Positioning the passband around 60 MHz allows that component to reach the amplifier while reducing components outside the passband. Figure 3 compares the harmonic components before and after filtering. The filter reduces the unwanted components without eliminating them completely.

The filter is connected between active stages. The limiter’s effective drive impedance and the input loading of the output amplifier both contribute to its response. ERD selects the filter and its surrounding circuitry together so that the selected harmonic drives the next stage under the intended conditions. [1, p. 3], [2, p. 2]

Harmonics Generated by the Output Amplifier

An ideal linear amplifier scales a sinusoid without changing its shape. A nonlinear transfer characteristic changes the shape and therefore its harmonic content. This can occur even when the waveform applied to the amplifier is sinusoidal. A simple cubic model makes the mechanism visible without requiring a particular amplifier circuit.

Let the selected frequency be fₒ = 3fᵢ, where fᵢ is the original input frequency. Apply $v\left(t\right)=A\cos \left(2\pi f_{o}t\right)$, where A is the sinusoid’s peak voltage, to the illustrative transfer relation

Here y(t) is the model’s output voltage; a₁ is a dimensionless linear coefficient and a₃ is a cubic coefficient with units V⁻². Substituting the sinusoid into (1) and expanding the cubic term separates the two frequency components:

The first term in (2) is at the desired output frequency fₒ. The second is at 3fₒ, or nine times the original input frequency. Thus, a stage driven at 60 MHz can produce a new component at 180 MHz. The output amplifier can generate additional harmonics. The output filter reduces these components to provide a clean sinusoidal signal at three times the input frequency.

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Filtering the Output Signal

The output filter passes the required signal around fₒ while attenuating unwanted components in the amplifier’s output. In the example above, it passes 60 MHz and reduces the component at 180 MHz. Reducing that harmonic makes the waveform delivered to the load more nearly sinusoidal. The residual depends on both the harmonic present before the filter and the filter’s transmission at that frequency.

The cubic model isolates one mechanism. An actual active stage can contain other nonlinear terms and can also carry residual components from the preceding circuitry. The output filter acts on that combined spectrum. [1, p. 4], [2, pp. 3–4]

Driving the Output Filter and Load

The amplifier supplies current and voltage to the output filter and load interface. Filter insertion loss and the fitted resistive pad reduce the level between the active stage and the output connector. The pad also establishes loading, while coupling elements separate the DC conditions. These elements are designed with the specified external load connected, so their combined response determines the delivered signal. [1, p. 4]

For a 50-ohm receiving circuit, the relevant level is the signal delivered at the module’s output interface into that load. Evaluating the module with the intended source and load accounts for the loading effects present in the application.

The two filters therefore have complementary functions. The first selects the desired third harmonic for amplification. The second reduces unwanted harmonic content in the amplified waveform before it reaches the load. The FM300 incorporates both filters, together with the conditioning and drive circuitry that connects them.

References

1. Esterline Research & Design, More than a multiplier: FM300 Product Overview, FM300-OV, Rev A, 7 October 2026.
2. Esterline Research & Design, More Than a Multiplier: What Makes a Frequency Tripler Usable?, TA-101, Rev –, 11 October 2026.
3. Esterline Research & Design, Fixed-Frequency and Broadband Multipliers: Filtering, Coverage and Integration, TA-102, Rev –, 16 October 2026. Figure 5 on page 4 is the graph-treatment reference for Figures 3 and 4 here; their spectra are newly drawn for this explanation.
4. Esterline Research & Design, FM Transfer and Amplitude Limiting, AN-101, Rev –, 7 October 2026.