Multigain amplifier optimizes sensor matching

By designing an amplifier

Nick Shakhtinov, PRI Automation -- EDN, January 6, 2000

Many applications requirea transferfunction in a narrow window of interest for a sensor's signal to work effectively or for the signal's interface with an A/D converter to match the full digital range of the converter. Meanwhile, the schematic diagram for the transfer function should be simple and cost-effective.

You can create the desired transfer function of a signal in many ways, depending on the design criteria and the required specifications. Some simple signal-conditioning circuits provide multigain amplification for dc or low-frequency signals.

The transfer function can consist of several signal-dependent compressing zones and one amplifying zone with different transfer coefficients in each zone. In a common case, the transfer function consists of two linear parts with the different transfer coefficients in the dc compressing and amplifying zones (Figure 1).

The output signal of a sensor is the input signal, V_IN, for the amplifier, whereas V_OUT is the output signal of the amplifier. The amplifying transfer coefficient, G_A, corresponds to the input signal within the (V_IN2–V_IN1) interval. The compressing line, as the transfer coefficient, G_COMP, ends at the breakpoint, B. This breakpoint could be anywhere along the amplifying line, depending on the compressing transfer coefficient. V_SAT is the output saturation voltage of the amplifier. Figure 2 represents the circuit that performs the transfer function of Figure 1. This dual-gain dc amplifier consists of two conventional noninverting operational amplifiers with negative feedback. The purpose of amplifier A_C is to create an active feedback and a closed loop with the feedback factor >1. The output voltage of amplifier A_A could be less than its input voltage, and the gain is less than unity, depending of the value of beta. This configuration converts the amplifier into a compressor. When the output voltage of the amplifier A_C reaches the level of saturation, the active feedback is switched off, and amplifier A_A continues to work in a common amplifying mode with a common passive negative feedback network, which resistors R_FA2, R_FA1and R_COMP determine. Thus, the breakpoint, B, is the critical point, when the compressing zone ends and the amplifying zone starts.

Figure 3 illustrates the relationship between amplifier A_A and compressor A_C, where G_C is the gain of compressing amplifier A_C, and point S is a saturation point of this amplifier. The breakpoint, B, on the transfer function corresponds to the saturation point S of the compressor A_C.

You can shift saturation point S of amplifier A_C to any side along the saturation line between points S_I and S_U by changing the gain G_C. Breakpoint B then shifts its place along the amplifying line, G_A, between points V_IN1 and S_U, according to the position of the point S. Point S_I corresponds to an infinite gain value for G_C, and point S_U corresponds to a unity gain for G_C.

The transfer function of Figure 4 is useful for window amplification of dc signals, especially for digitizing these signals. The window could be narrow to magnify and process only a small portion of an input signal. The output magnitude of the window ranges from a value close to zero up to the saturation voltage. The compressing zone (from V_IN=0 to V_IN1) is a line with a transfer coefficient equal to zero, corresponding to an infinite gain of the compressor. In reality, the gain, G_C, could be big enough without excitation problems to make a transfer coefficient close to zero. You need to determine the amplifying window size and position within the full range of the input signal, according to your required specifications. The most important parameters of the window amplifier are the width of the window, the position of the window, the gain of the window, and the transfer coefficient of the compressing zone.

The width of an input signal window (V_IN2–V_IN1) and the position V_IN1 depend on the physical characteristics of the input signal and your required measurement resolution. The preliminary value of the gain G_A of the window or the transfer coefficient of amplifier A_A should satisfy the expression:

Therefore, knowing the gain, G_A, you can calculate the value of resistors R_FA1 and R_FA2. The value of the compressing feedback resistor R_COMP is:

Once you know R_FA2 and the parallel resistance of R_FA1 and R_COMP, you can precisely calculate the value of G_A. Thus, the value of R_COMP depends on the position of the amplifying window along the V_IN axis. On the other hand, variations in R_COMP values give different positions of the amplifying window (Equation 2 and Figure 5). In the case of the infinite value of R_COMP, the value of V_IN1 becomes equal to zero because of elimination the compressing feedback. The values of other compressing resistors in Figure 5 are related by:

R_COMP1>R_COMP2>R_COMP3>R_COMP4.

Using R_COMP as a controlled resistor, you can scan the full range of an input signal with a magnifying window for automatic-calibration or for teaching-mode purposes.

The last important parameter is the transfer coefficient of the compressing zone. The dynamic range, D_WIN, of an output signal of the window amplifier is:

where V_OUTMIN is a minimal output voltage or a breakpoint, B, on the transfer function of Figure 4. A value of 40 to 60 dB for D_WIN is good enough for the dynamic range of an amplifying window. You can find the value of V_OUTMIN for a chosen value of dynamic range D_WIN. In this case, breakpoint B is close enough to the point V_IN1, and transfer coefficient G_COMP should be:

The gain of the compressor G_C is:

Example makes the idea clear

The following example shows a practical implementation of the window amplifier. The assumed specifications are:

• The range of an input dc signal is 0 to 100 mV; the window of interest is 75 to 89 mV (to get a resolution 1V/1 mV).

• The load resistance of the window amplifier is 10 kW.

• The power supply is ±15V.

• The operational amplifier is an LF347.

• The positive saturation voltage of LF347 is 1V with ±15V power and 10-kW load resistance.

Determine the gain G_A of the window using Equation 1:

The value of the resistor R_FA1 should be 1 kW, and the value of resistor R_FA2 (for the noninverting amplifier) should be 999 kW. The value of the compressing feedback resistor R_COMP, according to Equation 2, is:

Thus, the final value of G_A is 1004W when you consider resistor R_FA2 and the parallel combination of resistors R_FA1 and R_COMP.

Next, assume that the dynamic range, D_WIN, from an output signal is 50 dB. Then, the ratio of V_SAT to V_OUTMIN is 316.2, and V_OUTMIN should be 44.27 mV, according to Equation 3. To provide this value of V_OUTMIN, the compressing transfer coefficient, G_COMP, from Equation 4 should be:

Thus, the gain of amplifier A_C in the compressing zone is less than 1. The gain, G_C, of compressor A_C is defined according to Equation 5.

With the value of the resistor R_FC1 at 1 kW, the value of the resistor R_FC2 (for the noninverting amplifier) should be 314.76 kW. Figure 6 offers the final circuit for the desired specification with all calculated resistors rounded to the standard resistor values; V_IN is a variable low-voltage dc source.

The empirical measurements in the static mode gave these results:

• The input signal ranges from 75.5 to 90 mV, and the input window is 14.5 mV.

• The output signal ranges from 49 mV to 14V, meaning that the real dynamic range, D_WIN, is about 49 dB. In actual practice, the reliable linear range of the output window could be about 95% of the measured output range (V_OUTMIN and V_SAT) because of a nonlinear transition at breakpoint B (Figure 4) and at the point of a saturation voltage.

If you put a sawtooth waveform signal into the input of the amplifier, you would observe the output-window swing for the circuit (Figure 7, Figure 8, Figure 9, Figure 10, and Figure 11). The peak input voltage for the lower trace is 100 mV, and the upper trace shows the output swing at 5V/div.

You can shift the window swing by changing the value of the resistor, R_COMP. You can see the position of the output window determined by resistor R_COMP=300 kW (Figure 8). Measurements in the static mode yielded these results:

• The input signal ranges from 47 to 61.6 mV. The input window is 14.6 mV.

• The output signal ranges from 50 mV to 14V.

With the position of the output window set by resistor R_COMP=866 kW (Figure 9), the measurements in the static mode give these results:

• The input signal ranges from 16.5 to 31.2 mV; the input window is 14.7 mV.

• The output signal ranges from 51 mV to 14V.

Thus, in practice, you can get a nearly parallel shift of the window by changing the value of R_COMP. A slight difference exists between the windows because of the different values of R_COMP. A parallel combination of resistors R_FA1 and R_COMP slightly changes gain G_A of amplifier A_A (Figure 2).

You could establish a similar parallel shift by an offset of amplifier A_A for a negative input; Figure 10 and Figure 11 show the response of the dual-gain amplifier with a low gain G_C of compressor A_C.

Figure 10 represents the response of the amplifier, where R_COMP=187 kW, and R_FC2=1 kW. The output voltage at breakpoint B (Figure 1) is 7V. Figure 11 shows the output signal of the same circuit, where R_COMP=300 kW. The voltage of the breakpoint is 7V in this case, as well.

You can design multigain amplifiers with multicompressors connected in parallel. Compressors should have different gains; otherwise, the combined transfer coefficient G_COMP could be one extended straight line. For example, you could have a triple-gain amplifier with two compressors (Figure 12). Compressor A_C1 has a gain of 11, and compressor A_C2 has a gain of 2; both compressing feedback resistors have values of 475 kW. Measurements demonstrated a first breakpoint at 1.3V and the second breakpoint at 7.1V. Figure 13 shows the transient response of the amplifier for a 100-mV sawtooth input signal.

A compressing zone consists of two linear parts. The lower part of the output response corresponds to compressor A_C1 with the highest gain, and the upper part of an output response is an amplifying zone, corresponding to the amplifier A_A. Thus, you can achieve a nonlinear output transfer function by using a number of paralleled linear stages (compressors), each having different gain.

As a design guideline for applications with a single power supply, use operational amplifiers that have an output swing from rail to rail and an input common-mode range that includes the ground. Because of the zero-in, zero-out performance of such amplifiers, the output dynamic range could be high. A dual-gain window amplifier could be useful as the signal-conditioning circuit for the extraction of the meaningful information in the higher part of the range of analog, real-world variables.

Author info

Nick Shakhtinov is a senior electrical engineer at PRI Automation (Billerica, MA), where he designs systems for semiconductor factory automation. He has an MSEE from Vilnius State University (Lithuania).