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# FAQ - Hardware

#### Q1.  How can I Make Spectral Display mode in my 7265 lock-in work properly?

We are really sorry about this bug but there is an easy solution. Turn off the instrument and then press the front panel SET key. Keep this pressed while you turn on the instrument and, once the main display has appeared, release it. This process causes the internal memory to be reset and enables Spectral Display. It is only necessary to do this process once - the mode will work properly thereafter.

#### Q2.  How do I choose the right time-constant in my experiment?

Normally you want the time constant to be several 10's or 100's of periods of the reference cycle. So with a typical 2 kHz chopper frequency you might use a time constant (TC) between 10 and 100 ms. Remember that it is the averaging caused by taking many cycles of the reference waveform multiplied by the signal input that allows the noise to be rejected. The TC setting should really be defined by how long you are prepared to wait for a valid output reading following a step change in the input signal. So if you have a scanned system that takes say 10 points of data per second, you need the measured output to have settled within a 100 ms period. This in turn defines a TC of 10 or 20 ms, on the basis that you need between two and five time-constants to get a valid reading.

If you are using the curve buffer in our models 7225, 7265 or 7280 to log the output readings then this time of 100 ms also defines the sampling rate. If you wanted to see just the data at each scan point you would use a 100 ms time per point, but if you wanted to see how data changed during the scan you might use 10 or 20 ms.

#### Q3.  How do your dual-phase lock-in amplifiers calculate signal magnitude and phase?

The lock-in calculates the magnitude output by using the following equation:
MAG = SquareRoot( (X * X) + ( Y * Y) )

and the signal phase using a form of Arctangent algorithm:

PHA = ArcTangent( Y/X) when X is positive and
PHA = ArcTangent( Y/X) + 180 when X is negative

Phase (when using the non floating-pont PHA command, i.e. without a following dot) is reported in centidegrees, so a value of say -4523 is equal to -45.23 degrees.

Using the above formula and the reported values of X and Y gives:

MAG = SquareRoot( (-9169 * -9169) + ( 3993 * 3993) )
= 10000
which agrees with the MAG value from the lock-in, and

PHA = ArcTangent(3993/-9169) + 180 (because X is negative)
= ArcTangent(3993/-9169) + 180
= 156.47 degrees
which agrees with the PHA value from the lock-in.

When using Excel to perform signal phase calculations on raw X, Y values, use the function ATAN2( X, Y) rather than ATAN(Y/X). The former works in the same way as the algorithm in the lock-in. To convert the response from these functions, which is in radians, into degrees, multiply by 180/pi

#### Q4.  How do your dual-phase lock-in amplifiers calculate signal magnitude and phase?

The main ADC in Eclipse runs at 500 MSa/s. But since it also generates the trigger, it can govern the position within the basic 2 ns interval at which the sample and hold circuit actually samples the signal, using a trigger delay circuit. Hence when set to the 500 ps sample time, the first sweep will be done at a zero delay, the next at 500 ps, the next at 1 ns and the last at 1.5 ns. The resulting curves are then spliced together to give a curve with an effective sampling rate of 2 GSa/s - the only disadvantage being that four times as many triggers are required than would be the case with a 2 GSa/s ADC.

#### Q5.  Could you tell me which of your light choppers can work in a horizontal position?

Our light choppers can be used in any orientation.

#### Q6.  I am using an Indium Arsenide detector which has a shunt impedance of 842 ohms and want to know if it is necessary to use a preamplifier with this detector going into a 5209 lock-in.

You will not harm anything by connecting it straight to the input. I suspect that it is a current source, so you should try to use the 5209's B input and set the lock-in to current input mode (10E6 or 10E8 ranges). If the detector requires a bias, then avoid voltages greater than about 30V DC to protect the input, and only apply the bias after connecting the detector to the lock-in.

#### Q7.  When using the model 5210 to measure the phase angle of a capacitor, is it necessary to use an external source of signal (let's say 10 mV at 1 kHz frequency) or I can use the signal (10 mV at 1 kHz) taken from the internal oscillator of 5210 (OSC OUT connector) and apply that to the capacitor which I want to measure ?

You can certainly use the internal oscillator as a source of signal for your experiment. However you may need to take account of its output impedance which is about 910 ohms (not the 600 ohms quoted on most front panels). You should also measure the actual output voltage, since although the attenuator in the instrument allows 1 mV increments, the actual increments are not exactly that size.

#### Q8.  I have a question regarding how fast the 7265 can acquire the amplitude measurements from a chopped light experiment running at 100 Hz. One of our tests may require making multiple amplitude measurements as fast as we can. Could you tell us how fast the 7265 can give us these amplitude measurements?

You are going to be limited by the chopping frequency. The lock-in multiplies this by a 100 Hz sine wave to generate signals at DC and 200 Hz, and the output filter then gets rid of the 200 Hz signal. Hence the output filter must be set to a time-constant setting that is long enough to reject the 200 Hz signal. Typically this means using a TC of at least 10 ms and probably 20 or even 50 ms at 12 dB/octave slope. But the time response of the output filter also limits the number of useful data points you can acquire per second. As a rule of thumb, you need to allow between three and five time constants for the lock-in's output to settle following any change in the input, so at 10 ms TC this means a probable data collection rate of 20 Hz (i.e. 50 ms per point). This is one reason why people try to use higher frequencies.

If you increase your chopping rate to say 500 Hz, then you can increase the sampling rate. Of course you are limited in the end by the mechanics of the blade and the frequency response of the detector. The maximum rate at which the lock-in can output measurements depends on the computer interface, but in the case of the 7265 is 200 Hz max (5 ms per point) when using GPIB and somewhat lower when using RS232 (maybe 80 - 90 Hz). If you store data to the instrument's 32,768 point curve buffer first and then transfer it, the maximum rate is 800Hz.

#### Q9.  How can I upgrade my 7280 to allow dual reference mode operation at 2 MHz? At present it only works to 20 kHz in this mode.

The upgrade requires the entry of an "unlocking code". In order to get this, we need the instrument's serial number and a purchase order for the upgrade (model 7280/98). We will then release the code number, which will enable the option that is already present, but inoperative, in the instrument's firmware. Hence it is not necessary for your unit to be physically returned to us for the upgrade.

#### Q10.  I have a question concerning the output impedance of your 5184 preamp. The quoted output impedance is 450 ohms and it can drive 1 Mohm to 50 ohms. Does this cause any attenuation when driving 50 ohms?

The output impedance of 450 ohms will cause an output attenuation depending on the load. If the load is say 1 Mohm then the 450 ohms will be negligible by comparison and so will have no effect. At a load of 450 ohms the output will be half what would be achieved into 1 Mohm; at a 50 ohm load it will be one tenth.

#### Q11.  How can I use a 7265 to measure a noise power density specturm?

A lock-in amplifier produces a DC output for signals at the input that are phase-coherent with the reference. Signals at frequencies close to the reference appear at the output as beat frequencies at the difference between signal and reference frequencies, with these frequencies being attenuated by the output time-constant. Hence in may ways the lock-in can be considered as a narrow band-pass filter with a center frequency set by the reference and a bandwidth set by the time constant, with the additional characteristic that output frequencies are translated to being near DC.

In a dual phase instrument, when the Y-output is maximised the DC component of the Y output is zero. Hence if the Y output is passed to a true RMS - DC converter then the output of this will be proportional to the noise on the Y output, and thus also to that present at the input within the bandwidth set by the time constant. The value needs correcting for the measurement bandwidth to derive a noise reading in volts or amps per root hertz. The 7265 can be set to display a noise reading directly, so you can directly measure the noise at any frequency (up to 60kHz) simply by setting the lock-in to internal reference mode and the frequency as required. The measurement bandwidth can be changed by changing the time constant, but if the noise spectral density is reasonably uniform then the actual bandwidth (typically at most a few hertz) is not significant.

If you want to measure a noise spectrum (rather than noise about one frequency) then you need to arrange to step the oscillator frequency over the required range and record the noise at each step. Our Acquire data acquisition software can do this - try the free demo copy from this website.