Calculator Inputs
Formula Used
The calculator models the lock in output filter as cascaded first order low pass stages. The cutoff frequency is:
fc = 1 / (2π τ)
The normalized filter gain at each frequency is:
H(f) = [1 + (f / fc)²]^(-n / 2)
The phase shift from the output filter is:
φ(f) = -n tan⁻¹(f / fc)
The full gain chain is:
Total Gain = Preamp Gain × Mixer Efficiency × cos(Phase Error) × H(f)
The output amplitude is:
Output Vrms = Input Vrms × Total Gain
The cascaded -3 dB frequency is:
f-3dB = fc × √(2^(1/n) - 1)
How to Use This Calculator
- Enter the measured input signal amplitude in millivolts RMS.
- Add the preamp gain and mixer efficiency from your instrument settings.
- Enter the reference phase error if the signal is not perfectly aligned.
- Set the lock in time constant and output filter order.
- Select the start and stop frequency for the sweep.
- Choose a linear or logarithmic sweep scale.
- Press the calculate button to view gain, phase, output, and SNR.
- Use the CSV or PDF option to save the results.
Example Data Table
This example uses 10 mVrms input, 100 V/V preamp gain, 0.5 mixer efficiency, 0.1 s time constant, and a 2 pole filter.
| Frequency Hz | Filter Gain | Total Gain V/V | Gain dB | Phase deg | Output Vrms |
|---|---|---|---|---|---|
| 0.10 | 0.9961 | 49.805 | 33.944 | -7.19 | 0.498 |
| 1.00 | 0.7170 | 35.850 | 31.090 | -64.28 | 0.358 |
| 10.00 | 0.0247 | 1.235 | 1.835 | -162.0 | 0.0124 |
| 100.00 | 0.00025 | 0.0127 | -37.93 | -178.2 | 0.000127 |
Understanding Gain vs Frequency in a Lock In Amplifier
What the Sweep Shows
A lock in amplifier extracts a weak signal from a noisy background. It multiplies the input by a clean reference signal. The mixed output then passes through a low pass filter. This filter controls the final response. The gain is high at slow variations. It falls when the frequency rises above the filter bandwidth.
Why Time Constant Matters
The time constant sets the response speed. A large time constant gives stronger noise rejection. It also makes the output slower. A small time constant follows faster changes. It rejects less noise. The correct value depends on the experiment. Sensitive measurements often need a slower setting.
Filter Order and Roll Off
The filter order controls the steepness of the gain curve. A first order filter rolls off gently. Higher order filters reduce unwanted frequencies faster. They also add more phase shift. That phase shift can matter when timing is important. The plotted curve helps compare these effects clearly.
Phase and Output Level
Phase error reduces measured amplitude. A perfect phase match gives maximum output. A ninety degree error can almost cancel the signal. This calculator includes that loss. It also estimates output voltage. That helps avoid overload. The output limit percentage warns when settings are too large.
Noise and Bandwidth
Lock in performance depends on bandwidth. Narrow bandwidth reduces random noise. The equivalent noise bandwidth gives a useful estimate. Lower bandwidth improves signal stability. It also increases settling time. Use the SNR estimate as a guide. Actual laboratory noise can differ from the model.
Practical Use
Use a logarithmic sweep for broad frequency ranges. Use a linear sweep near a known cutoff. Compare gain, phase, and output together. A good setting gives enough signal. It also keeps noise and overload under control. Export the table when you need a lab record.
FAQs
What does gain vs frequency mean here?
It shows how the lock in output gain changes as the signal or modulation frequency changes. The curve mainly reflects the selected time constant and filter order.
Why does gain fall at higher frequency?
The output low pass filter rejects fast variations. As frequency rises beyond the cutoff region, the filter gain drops and the measured output becomes smaller.
What is the role of the time constant?
The time constant controls bandwidth and settling speed. A larger value gives better noise rejection, but it slows the response to real signal changes.
How does filter order affect the curve?
Higher filter order makes the roll off steeper. It suppresses unwanted frequencies more strongly, but it also increases phase shift near and above cutoff.
Why include phase error?
A lock in amplifier measures the component aligned with the reference. Phase error reduces the detected amplitude by the cosine of the phase mismatch.
Is this model exact for every instrument?
No. It is a practical analytical model. Real instruments can use different filter shapes, scaling rules, reserve settings, and digital processing methods.
When should I use logarithmic sweep?
Use logarithmic sweep when the frequency range covers several decades. It gives more readable plots for cutoff, roll off, and wideband response studies.
What does output limit percentage show?
It compares the calculated output voltage with your selected output limit. High values suggest possible overload, clipping, or poor gain setting choice.