Programmable-gain amp achieves high gains

& -October 22, 2015

Most data acquisition systems with a wide dynamic range need some method of adjusting the input signal level to the analog-to-digital converter (ADC) to maximize use of the ADC’s full-scale input voltage range. To achieve this, a programmable-gain amplifier (PGA) or a variable-gain amplifier (VGA) is usually located between a sensor and its ADC, as shown in Figure 1. Additional signal conditioning may take place before or after the PGA or VGA, depending on the application.

Figure 1  PGA in data acquisition system

 

When high gains are needed, the topology of the PGA circuit deserves extra thought. It is not advisable to use feedback resistors with a very high value (>1MO) due to noise and op-amp offset current. In addition, for an inverting amp, high gain can result in low input resistance.

This Design Idea presents a PGA circuit which satisfies these conditions. Figure 2 shows the two versions, having eight digitally programmable gains.


Figure 2a  Inverting PGA circuit


Figure 2b  Non-inverting PGA circuit

 

Although the number of gains that can be implemented with these circuits is equal to 2n, where n is the number of used MOSFETs, it is only possible to implement n+1 independent gains.

Signals D1, D2, and D3 select the gain of the amplifier. The switches will typically be “logic level” MOSFETs with RDSon as low as possible (e.g., 2N7002P with RDSon (typ) = 1O  or IRLML2502 with a RDSon (typ) = 0.05O).

The independent gains that can be selected in the amplifier circuit shown in Figure 2a are:

       

Restrictions

For Figure 2a, when two or more MOSFETs are used, the MOSFET body diodes will start to conduct if the input voltage (vi) takes too large a value, distorting the output voltage of the amplifier. To avoid this, the following condition must be satisfied:

    

where vF is the body diode forward voltage of the MOSFET (vF > 0).

When only one MOSFET is used, the input voltage must fulfill the following condition to avoid body diode conduction:

    

The independent gains that can be selected in the amplifier circuit shown in Figure 2b are:

    

For Figure 2b, when using two or more MOSFETs, the body diodes will conduct if the input voltage (vi) takes too large a negative value. To avoid this, the following condition must be satisfied:

  

When only one MOSFET is used, the input voltage must fulfill the following condition to avoid body diode conduction:

   

Figure 3 shows a practical application of the circuit of Figure 2a. In this example, a PGA is used to amplify the output voltage (vi) of a circuit that integrates and filters the signal generated by a Rogowski coil.

 


Figure 3  AC measurement system based on a Rogowski coil

 

It has been assumed that the ADC that will sample the signal vo = k·i(t) has reference voltages of vref + = 2.5v and vref - = -2.5v, the Rogowski coil has a sensivity of 30µV/A, the integrator/high-pass filter has a gain equal to 1.2 = 1.64 dBs at 50Hz, and we want to measure AC currents in the following ranges: 1280Arms, 320Arms, 80Arms and 20Arms. According to the previous data, the gains that we should be able to select are: G0 = -38.363, G1 = -153.452, G2 = -613.808, and G3 = -2455.2. A simple method to calculate the resistor values is:

Ra3 = 300·RDS-on = 300·1O = 300O ? we set the smallest value of the Ra resistors to ensure that the value of RDS-on does not have a significant influence on the amplifier gains.

 

R2 = R3 = 2·Ra3·(G3-G0)/G0 = 37799.9 @ 37800 O

R1 = -4·Ra3·(-1+G3/G0)/G0 = 1970.6 @ 1970 O

Ra1 = Ra3·(G3-G0)/(G1-G0) = 6299.8 @ 6300 O

Ra2 = Ra3·(G3-G0)/(G2-G0) = 1260 O

 

The gains obtained with the calculated values are (theoretical values are shown in square brackets):

 

D3 D2 D1 = 0 0 0  ?  G0 = -38.3756  [-38.363]

D3 D2 D1 = 0 0 1  ?  G1 = -153.5025  [-153.452]

D3 D2 D1 = 0 1 0  ?  G2 = -614.01  [-613.808]

D3 D2 D1 = 1 0 0  ?  G3 = -2456  [-2455.2]

  

For a non-inverting design, the following method can be used to select resistor values that provide gains G0 = 38.363, G1 = 153.452, G2 = 613.808, and G3 = 2455.2:

  

The gains obtained with the calculated values are:

 

D3 D2 D1 = 0 0 0  ?  G0 = 38.3631  [38.363]

D3 D2 D1 = 0 0 1  ?  G1 = 153.4532  [153.452]

D3 D2 D1 = 0 1 0  ?  G2 = 613.8139  [613.808]

D3 D2 D1 = 1 0 0  ?  G3 = 2455.3  [2455.2]

 

Also see:

 

 

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