8.2.1.1 Design Requirements

The wide unity-gain bandwidth allows these parts to provide large gain over a wide frequency range, while driving loads as low as 2 kΩ with less than 0.003% distortion.

8.2.1.2 Detailed Design Procedure

Figure 39 is an inverting amplifier, with a 100-kΩ feedback resistor, R₂, and a 1-kΩ input resistor, R₁, and provides a gain of −100. With the LMV641, these circuits can provide gain of −100 with a −3-dB bandwidth of 120 kHz, for a quiescent current as low as 116 µA. Coupling capacitors C_C1 and C_C2 can be added to isolate the circuit from DC voltages, while R_B1 and R_B2 provide DC biasing. A feedback capacitor C_F can also be added to improve compensation.

8.2.1.3 Application Curve

Figure 40. High Gain Inverting Amplifier Results

8.2.2.1 Design Requirements

The low operating current of the LMV641 makes it a good choice for battery-operated applications. Figure 41 shows two LMV641s in a portable application with a magnetic field sensor. The LMV641s condition the output from an anisotropic magnetoresistive (AMR) sensor. The sensor is arranged in the form of a Wheatstone bridge. This type of sensor can be used to accurately measure the current (either DC or AC) flowing in a wire by measuring the magnetic flux density, B, emanating from the wire.

8.2.2.2 Detailed Design Procedure

In this circuit, the use of a 9-V alkaline battery exploits the LMV641’s high voltage and low supply current for a low-power, portable-current-sensing application. The sensor converts an incident magnetic field (through the magnetic flux linkage) in the sensitive direction, to a balanced voltage output. The LMV641 can be used for moderate to high current sensing applications (from a few milliamps and up to 20 A) using a nearby external conductor providing the sensed magnetic field to the bridge. The circuit shows a Honeywell HMC1051Z used as a current sensor. Note that the circuit must be calibrated based on the final displacement of the sensed conductor relative to the measurement bridge. Typically, once the sensor has been oriented properly, with respect to the conductor to be measured, the conductor can be placed about one centimeter away from the bridge and have reasonable capability of measuring from tens of milliamperes to beyond 20 amperes.

In Figure 41, U1 is configured as a single differential input amplifier. Its input impedance is relatively low, however, and requires that the source impedance of the sensor be considered in the gain calculations. Also, the asymmetrical loading on the bridge will produce a small offset voltage that can be cancelled out with the offset trim circuit shown in Figure 41.

Figure 42 shows a typical magnetoresistive Wheatstone bridge and the Thevenin equivalent of its resistive elements. As we shall see, the Thevenin equivalent model of the sensor is useful in calculating the gain needed in the differential amplifier.

Figure 42. Anisotropic Magnetoresistive Wheatstone Bridge Sensor, (a),
and Thevenin Equivalent Circuit, (b)

Using Thevenin’s Theorem, the bridge can be reduced to two voltage sources with series resistances. ΔR is normally very small in comparison to R, thus the Thevenin equivalent resistance, commonly called the source resistance, can be taken to be R. When a bias voltage is applied between V_EXC and ground, in the absence of a magnetic field, all of the resistances are considered equal. The voltage at Sig+ and Sig− is half V_EXC, or 4.5 V, and Sig+ - Sig− = 0. Bridges are designed such that, when immersed in a magnetic field, opposite resistances in the bridge change by ±ΔR with an amount proportional to the strength of the magnetic field. This causes the bridge's output differential voltage, to change from its half V_EXC value. Thus Sig+ - Sig− = Vsig ≠ 0. With four active elements, the output voltage is:

Equation 2.

Because ΔR is proportional to the field strength, B_S, the amount of output voltage from the sensor is a function of sensor sensitivity, S. This expression can rewritten as , where

A simplified schematic of a single op amp, differential amplifier is shown in Figure 43. The Thevenin equivalent circuit of the sensor can be used to calculate the gain of this amplifier.

Figure 43. Differential Input Amplifier

The Honeywell HMC1051Z AMR sensor has nominal 1-kΩ elements and a sensitivity of 1 mV/V/gauss and is being used with 9 V of excitation with a full scale magnetic field range of ±6 gauss. At full-scale, the resistors will have ΔR ≈ 12 Ω and 108 mV will be seen from Sig− to Sig+ (see Figure 44).

Figure 44. Sensor Output with No Load

Referring to the simplified diagram in Figure 43, and assuming that required full scale at the output of the amplifier is 2.5 V, a gain of 23.2 is needed for U1. It is clear from the Thevenin equivalent circuit in Figure 45 that a sensor Thevenin equivalent source resistance, R_THEV, of 500 Ω will be in series with both the inverting and noninverting inputs of the LMV641. Therefore, the required gain is:

Equation 4.

Choosing R₁ = R₂ = 24.5 kΩ, then R₄ will be approximately 580 kΩ. The actual values chosen will depend on the full-scale needs of the succeeding circuitry as well as bandwidth requirements. The values shown here provide a −3-dB bandwidth of approximately 431 kHz, and are found as follows.

Figure 45. Thevenin Equivalent Showing Required Gain

By choosing input resistor values for R₁ and R₂ that are four to ten times the bridge element resistance, the bridge is minimally loaded and the offset errors induced by the op amp stages are minimized. These resistors should have 1% tolerance, or better, for the best noise rejection and offset minimization.

Referring once again to Figure 41, U2 is an additional gain stage with a thermistor element, R_TH, in the feedback loop. It performs a temperature compensation function for the bridge so that it will have greater accuracy over a wide range of operational temperatures. With mangetoresistive sensors, temperature drift of the bridge sensitivity is negative and linear, and in the case of the sensor used here, is nominally −3000 PP/M. Thus the gain of U2 needs to increase proportionally with increasing temperature, suggesting a thermistor with a positive temperature coefficient. Selection of the temperature compensation resistor, R_TH, depends on the additional gain required, on the thermistor chosen, and is dependent on the thermistor’s %/°C shift in resistance. For best op amp compatibility, the thermistor resistance should be greater than 1000 Ω. R_TH should also be much less than R_A, the feedback resistor. Because the temperature coefficient of the AMR bridge is largely linear, R_TH also needs to behave in a linear fashion with temperature, thus R_A is placed in parallel with R_TH, which acts to linearize the thermistor.

8.2.2.2.1 Gain Error and Bandwidth Consideration if Using an Analog to Digital Converter

The bandwidth available from Figure 41 is dependent on the system closed loop gain required and the maximum gain-error allowed if driving an analog to digital converter (ADC). If the output from the sensor is intended to drive an ADC, the bandwidth will be considerably reduced from the closed-loop corner frequency. This is because the gain error of the pre-amplifier stage needs to be taken into account when calculating total error budget. Good practice dictates that the gain error of the amplifier be less than or equal to half LSB (preferably less in order to allow for other system errors that will eat up a portion of the available error budget) of the ADC. However, at the −3 dB corner frequency the gain error for any amplifier is 29.3%. In reality, the gain starts rolling off long before the −3 dB corner is reached. For example, if the amplifier is driving an 8-bit ADC, the minimum gain error allowed for half LSB would be approximately 0.2%. To achieve this gain error with the op amp, the maximum frequency of interest can be no higher than

Equation 5.

where

• n is the bit resolution of the ADC
• f_{−3 dB} is the closed loop corner frequency.

Given that the LMV641 has a GBW of 10 MHz, and is operating with a closed loop gain of 26.3, its closed loop bandwidth is 380 kHZ, therefore

Equation 6.

which is the highest frequency that can be measured with required accuracy.