Accelerometer Design

# Signal Conditioners

The charge signal of a piezoelectric sensor is a very particular output and cannot be electrically loaded by standard practice without impact on the signal itself. That is why we need an adapted signal conditioning. This is to deliver a low impedance electrical signal through a standard interface that can be loaded, shared and processed further.

## Charge Amplifier

Why would we need a charge amplifier? Could we not just as easily use a standard voltage amplifier?

The piezo element represents electrically a capacity which can store electric charge. If we “fill” the capacity with a charge (pico-Coulombs) a voltage builds up over the capacity.

The voltage U  will be   U = Q/C     or the charge stored     Q = C·U

Q = charge ; C = capacity

If we store a certain charge on a small capacity the voltage will be greater than if we would apply the same charge to a bigger capacity. (The above notation will be basic for the understanding of the function of a charge amplifier)

So far so good, we could easily use a voltage amplifier. However if we connect the piezo element to the voltage amplifier by a cable the total capacity becomes Ctotal = Cpiezo +Ccable , which means that the voltage drops significantly, particularly if the cable has a relatively big capacity compared to the piezo. If we use a cable with a different length or different internal capacity the voltage changes again.

Another potential problem we have seen is the discharge of the piezo at low frequencies due to the RC time constant which is given by the capacity and internal resistance of the sensor and cable (although the increasing capacity would help the problem somewhat).

We can avoid these problems by using a charge amplifier. “Charge amplifier” is a common term in electrical metrology but strictly speaking it does not amplify charge but it is rather a charge-to-voltage converter meaning it puts out a voltage which corresponds to the applied charge at the input.

Basically the charge amplifier consists of a high-gain inverting operational amplifier (op-amp) OP  with a MOSFET or J-FET input stage to achieve maximal input resistance. In the feed-back loop from the output to the inverting input we find a capacitor Cf . In parallel to the feed-back capacitor there is a

resistance Rf , the function of which we will see later. The non-inverting input is connected to ground. The sensor (through a cable) is also connected to the inverting input. The piezo element is depicted here by three parallel elements a current source, the internal resistance Rp   and the internal capacity Cp .

For simplification the circuit shown is single ended, one pole connected to ground.

Simplified charge amplifier with piezo element and connecting cable

### Function of the Charge Amplifier

Ideally the op-amp amplifies only the difference in voltage between the two inputs, the differential input voltage ΔUin. The output voltage Uout  of the op-amp with no external components is

Uout = -ΔUin·AOL

AOL  is the open loop gain of the amplifier. The magnitude of AOL  is typically very large (more than 100’000). This means even a very small voltage difference ΔUin  can drive the amplifier output to the maximum i.e. to saturation. With MOSFET input stages only a few pico-Amps flow through the inputs in this condition.

In a closed loop situation, with the feed-back capacitor Cf , the output voltage will take the value necessary to drive the voltage difference between the inputs towards zero. If the gain AOL  is high enough the inverting input will be practically at ground potential like the non-inverting input. This means the charge amplifier input is virtually short-circuited ! All input capacities including the cable and piezo element (Cc and Cp ) are held at virtual ground potential.

Now if the piezo element puts out a charge Qp  no voltage can build up and therefore (practically) no current will charge up the input capacities Cc and Cp. The piezo charge Qp , or more the corresponding current ip  (pC/seconds), starts to flow into the op-amp and drives the output voltage to a certain value -Uout. The feed-back capacitor Cf  converts the output voltage into a charge Qf = -Cf · Uout  which is also added to the input.

The op-amp will adapt the output voltage until  ΔUin =0  and thereby Qp = Qf = -Cf · Uout.

Rearranging, we get:

Uout  =  -1/Cf   ·  Qp

-1/Cf   is the “gain” or conversion factor of the charge to voltage converter

[1/Cf ] = V/C   (Volt /Coulomb)

### Virtual Capacity

Of course the virtual ground is not exactly at ground potential but at a small value ΔUin  above ground, if we assume a positive Qp .

We had Uout = - Qp/Cf  and regarding the amplification of the op-amp Uout  = - ΔUin · AOL

and therefore    Qp = ΔUin · Cf ·AOL

This means the charge amplifier behaves like a large virtual capacity Cv = Cf ·AOL.

Therefore the addition of a cable capacity which will be small compared to Cv does practically not influence the output voltage Uout. We can see now as well that the charge amplifier improves the discharge behavior of the piezo element. With a largely greater capacity Cv instead of Cp  the discharge time constant will be increased accordingly. However if we are looking for extremely low frequencies a good total resistance from the input to ground must still be guaranteed (Rp in parallel with Rc ), otherwise the leakage current due to the ΔUin  will be high enough to become dominant and let the output drift.

So far about the core function of the charge amplifier.

### Time Constant of the Charge Amplifier

The charge amplifier is basically an integrator or more precisely an integrating current to voltage converter. It integrates the input current pC/second and converts it into Volts. The circuit will sum up any differential input voltage over the time, no matter how small it may be. However the input voltage difference of a technical charge amp will never be exactly zero and therefore the output will be driven into saturation. For this reason there is a resistor Rf  in parallel to the feed-back capacity Cf  which will discharge it with the time constant T= Rf Cf . The charge amplifier is therefore not a pure integrator but becomes with this resistor a 1st order high-pass with a cut-off frequency

1

f = ––––––––

2π Rf Cf

For this reason a charge amplifier is not suitable for measuring static charges.

At higher frequencies Cf  is dominant and the output will be correct however at low frequencies Rf  will start to pull the output towards zero. So far we have also neglected the sensor and cable resistances Rp  and Rc  from the input to ground. At very low frequencies they start also to play their role. If Rp or Rc  is too small the integrator will start to drift into saturation.

High-quality devices achieve low cut-off frequencies of less than 0.1 Hz (with sufficiently high input resistances). Most laboratory charge amps have also a “quasi static” setting which allows theoretically static signals at least for a short time. However this needs extremely high insulation resistances and critical analysis of the results.

In practice, a charge amplifier contains normally additional circuit stages, such as high and low pass filters, integrators and level control circuits, as well as additional output stages to provide some standardized output signal.

## Integrated Electronics (IEPE)

In view of signal noise and ease of signal transmission a good place to put an amplifier is in the accelerometer itself. In fact it is quite common to place a small electronic inside the sensor housing when specifications like temperature and other environmental conditions allow. Over the years a certain specific technique has become the norm. This technique is called IEPE and stands for Integrated Electronics Piezo-Electric but there are also registered trade names like ISOTRON (Endevco), ICP (PCB), CCLD and DeltaTron (both B&K) or Piezotron (Kistler). The IEPE sensor electronics converts the high impedance signal of the piezo element into a low impedance voltage signal. We find charge to voltage converters but also so called voltage followers which put out the same voltage as applied to the input but with a low output impedance. With the conditioner mounted in the sensor we can use the piezo output voltage as there is no cable loading the piezo element. The complete IEPE circuit comprises a constant current source as a power supply, which is located at the far end of a coaxial connection cable. The IEPE circuit is a two wire system meaning that both supply current and output voltage are transmitted via just one wire besides the common return.

The basic design of such an IEPE consists in a simple MOSFET transistor, sometimes followed by a bipolar junction transistor (BJT). On the far end there is the constant current power supply.

The diagram shows the complete circuit. The piezo element is represented again with an AC current source ip and the elements Rp and Cp. The sensor built-in circuit consists of a MOSFET, a capacitor Cr  and a resistor Rt .

The remote power unit is

Typical IEPE circuit with piezo element, MOSFET, connecting cable and power unit

connected through a cable with the capacity Cc. From a DC power supply which must have sufficient compliance voltage (a battery or external source) a constant supply current isup  is released by the constant current diode D. Typical supply currents are in the range of 2 to 20 mA.

### Function of the IEPE circuit

The current through the MOSFET generates a constant bias voltage Ubias of typically 7 to 14 Volt depending on the supply current. This arrangement is called source follower circuit. The source follower has a very high input impedance and an output impedance in the order of 100 Ω, also depending on the supply current.

The MOSFET is used to act as a buffer amplifier. It is separating the whole circuit basically into two regions: The input side, dominated by ip and the transmission side, dominated by isup isup .

The AC voltage of the piezo element Up is present at the gate input (g) of the MOSFET and is added to the bias voltage Ubias . The voltage Us at the source terminal (s) follows the gate voltage (hence “source follower”). The gain of the follower together with the constant current diode is very close to unity.

Up = Ubias+Up  is always positive and oscillates around Ubias. In the power supply module the useful signal voltage Uout  is decoupled from Us  by the capacitor Cd  and turned into a pure AC signal again.

When the piezo element puts out the Charge Q  the current ip = dQ/dt  is flowing and charges the capacitance of the piezo Cp but also Cr  and Cg . The output voltage Up  takes the value

Q

Up = ––––––––––

Cp+Cr+Cg

Cr and Cg are a given characteristics of the piezo element respectively the MOSFET. The range capacitor Cr  allows adapting the sensitivity (downwards only). Normally we can neglect the gate capacitance Cg  because it is only a few pico-Farads however some piezo elements such as Quartz have extremely small capacities and Cg  may then influence the sensitivity.

In parallel to the range capacitor Cr  we find a timing resistor Rt  which allows controlled discharging of the capacitors on the input side forming a high pass filter with the time constant T = Rt · (Cp+Cr+Cg).

Boundary conditions to observe

On the transmission side of the circuit we have to check on the cable capacity Cc . Operation over long cables may affect the frequency response or introduce distortion when the supply current is insufficient to drive cable capacitance. Here is a proposition to estimate the limit frequency fc . We assume the constant current diode to be a resistor R  that delivers the same current isup . It is also assumed that the IEPE circuit needs 1mA so the current available to charge the cable capacity is ic = isup -1 mA. The max current is needed to reach the signal peak Voltage Upk at the limit frequency fc. With the time constant R·Cc  the limit frequency f for a -3db signal reduction becomes fc = 1 / (2π· R·Cc ).

To get rid of we take R = Upk / ic  = Upk / (isup -1 mA)  and we get

isup -1 mA

fc = ––––––––––

2π Cc Upk

For example:

With 50 meters of cable at 100pF/m we get Cc =5’000pF. We assume Upk = 5V and isup = 4mA

4 -1  mA

fc = ––––––––––––––  = 19.1 kHz

2π · 5000pF · 5V

This is only a rough estimation and -3dB quite a lot. It is therefore recommended to use only half of the calculated bandwidth i.e. about 10 kHz in the example. The suppliers normally provide nomograms to determine the limit frequency. We can retain: The higher the supply current the longer the possible cable length.

When looking at very low frequencies another detail might be important: The decoupling capacitor Cd together with the input resistance of the follow-on instrument will form yet another RC time constant, this time a high-pass filter. With typically 10 μF for Cd  we need a minimum 1 Megohm input impedance on the follow-on equipment to obtain a time constant of 10 seconds. This also assumes a MOSFET output impedance of <100 Ω. As a general rule, the coupling time constant should be at least 10 times larger than the sensor time constant.

Summary

Though the IEPE circuit may be extremely simple there are a few considerations needed in order to get it right. Of course there are also more sophisticated signal conditioners which have a standard interface for the transmission signal and include also the power supply so there should be no hassles.

The cable doesn’t need to be especially low noise like for a charge transmission. A standard coax will do it. Due to the simplicity these built-in circuits are very reliable also in rough conditions. There are IEPE sensors with surprisingly extreme temperature capabilities from cryogenic (5°K) up to 175°C or even 200 °C are claimed.