Front-end hardware depicted in Figure 3.7 consolidates two different circuits:
inverting operational amplifier and transimpedance amplifier. The non-inverting operational amplifier isolates the measuring load from the excitation signal generator circuitry. While the transimpedance amplifier converts the cur-rent flowing through the load to a voltage signal with a known proportional factor that is defined by the feedback resistor.
TransImpedance
Rf (Feedback Resistor) Vext
VTI,O
VTI,Iov
Iz ITI,Ib
Figure 3.7: Front-end circuit based-on Three-electrode topology Using negative feedback in the non-inverting operational amplifier causes the load draws very little current from the excitation source and leads to less disturbance in impedance measurement. In Figure 3.7, the excitation signal is applied to the non-inverting input. The output of non-inverting operational amplifier, op-amp mirrors the same voltage level as its input voltage. Since volt-ages on input pins on transimpedance op-amp are in the same levels, the total voltage drop on load is equal to the excitation voltage level. Theoretically, the input impedance of an Op-amp is considered infinite. Therefore, it is assumed that the amount of input current passing through the Op-amp inputs are close to zero. Inevitably, the current of the load passes through the feedback resistor of the transimpedance Op-amp. This simple topology provides a full compact solution to measure the impedance of the load precisely.
Accuracy of the response voltage determines the measurement accuracy.
The accuracy depends on the characteristics of the op-amps. Ideally, the to-tal amount of the current passes through the feedback resistor of the tran-simpedance circuit. However, in the real world, a small amount of the current flows into both inverting and non-inverting inputs of Op-amps. This leads to disturbances in impedance measurement by creating a bias voltage across the measuring impedance. Many op-amps take advantage of a built-in input bias cancellation circuit.
Moreover, use of an input bias current resistor, specified as a value of impedance and feedback resistor in parallel, ensure the same level of input bias current on both inputs where may eliminate output error. The same principle applies to the non-inverting operational amplifier stage. The supply current can leak back into inverting input of the Op-amp. A better Op-amp features the less possible input bias current in the range of few nano amps to some femto amps.
Small-signalbandwidth[MHz] Gainbandwidthproduct[MHz] InputBiasCurrent SupplyCurrent(Max)[mA] OperatingSupplyVoltage[Vp−p] Productpackage
LM7171 200 2.7µA–12µA 9.5 5.5 - 36 PDIP-8/
SOIC-8 OPA1S2385 250 100 3pA–50pA 9.2 2.7 - 5.5 SON-10 LTC6268-10 4000 3f A–4pA 16.5 3.1 – 5.25 SOIC-8
Table 3.2: Operation amplifier comparison.
The wideband binary excitation signal is a pulse shaped signal which is com-posed of several frequency components. Gain bandwidth product and Small-signal bandwidth parameters of an Op-amp controls the shape of a square wave-form. All frequency components of the input signal shall pass through the flat frequency response of the Op-amp with minimum attenuation.
The specification of the front-end electronics suggests a 5 MHz unity-gain bandwidth for impedance measurement. By this, three Op-amps are candidates for prototyping. Op-amp characteristics are listed in Table3.2.
According to the Table3.3, the premium choice will be LTC6268-10 from Lin-ear technology that offers overestimated and generous bandwidth option with pico-Ampere input bias current and therefore achieving an optimum accuracy of the current measurement. OPA1S2385 combines high bandwidth, FET-input operational amplifiers with a fast SPST CMOS switch that specifically designed for application for capturing fast signals. Low input bias current and voltage noise make it possible to amplify extremely low-level input signals for maxi-mum signal-to-noise ratio. Both LM7171 and OPA1S2385 products from Texas Instruments provide sufficient bandwidth, but OPA1S2385 offers around 1000 times lower bias current. LTC6268-10 and OPA1S2385 are optimized for low-voltage operations.
Although low input bias current is an essential parameter to be considered in the ultimate design of the impedance measurement circuit, high operating voltage range, sufficient bandwidth and PDIP package of LM7171 make it a per-fect choice for prototyping on a breadboard. The Lm7171 provides a very high slew rate at 4100V /µsand unity-gain bandwidth of 200 MHz while consum-ing 6.5mA in typical mode. Operatconsum-ing voltage of±15V allows for large signal swings and provide greater dynamic range and signal-to-noise ratio. These
inte-Step Response
Small-Signal Large-Signal
LM7171 Av=−1 Vs=±5V
OPA1S2385 RL= 1KΩ connected to Vs/2
Vo=VCM=Vs/2
LTC6268-10 See image captions for more details.
Table 3.3: Operation amplifier comparison.
grated circuits are cross-compared with respect to small-signal and large-signal step response.
The output voltage of the transimpedance amplifier in Figure3.7 is formu-lated as:
VT I,O =−Rf(IZ−IT I,Ib) (3.3.1)
IZ =VExc−VT I,Iov
Z (3.3.2)
Where,
VT I,O : Transimpedance output voltage Rf : Transimpedance feedback resistor
IZ : The amount of the current passes the impedance IT I,Ib: Transimpedance input bias current
VExc : Excitation voltage signal
VT I,Iov: Transimpedance input offset voltage Z: Measuring impedance
From 3.3.1 and 3.3.2, the compact formula can be gives as:
VT I,O =−Rf
VExc−VT I,Iov
Z −IT I,Ib
(3.3.3) Considering negligible input bias current and input offset voltage for the operational amplifier, the formula can be written in short form of:
VT I,O =−Rf VExc
Z
(3.3.4) Hence, feedback resistor is calculated as:
Rf=Z
VT I,O
VExc
(3.3.5) And impedance is given as:
Z =−Rf
VExc
VT I,O
(3.3.6)
Value of the feedback resistor in transimpedance circuit should be deter-mined according to three factors: 1) Excitation signal voltage range, 2) Impedance value range within the desired frequency range and 3) Desired output voltage range. Although the fast analog input can be configured for small signals±1V to achieve better reading accuracy, in order to use full output swing range of LM7171, the analog input is switched to±20V range. In practice, an embed-ded voltage limiter in Red Pitaya board carries out this operation. Factors 1 and 2, basically define the expected range of current passes through the measuring impedance.