“Many kinds of precision applications have the function of sensing light, and can convert light-sensing information into useful digital signals. The designer must carefully correct the circuit instability of the application front-end with the help of the Bode diagram.

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Many kinds of precision applications have the function of sensing light, and can convert light-sensing information into useful digital signals. The designer must carefully correct the circuit instability of the application front-end with the help of the Bode diagram.

Figure 1. This two-Transistor circuit is a high-gain amplifier used to light up LEDs.

At the front end of the system, the preamplifier converts the current output signal of the photodiode into a usable voltage level. Figure 1 shows the front-end circuit of the system, which consists of a photodiode, an operational amplifier, and a feedback network. The transfer function of the system is:

Among them, AOL(jw) is the amplifier open loop gain of frequency; b is the system feedback coefficient, namely 1/(1+ZIN/ZF); ZIN is the distributed input impedance, namely RPD||jw(CPD+CCM+CDIFF ); ZF is the distributed feedback impedance, namely RF||j (CRF+CF).

Bode diagrams are a useful tool for determining stability. The Bode diagram for this design includes the amplifier’s open loop gain and 1/b curve. Some of the system factors that determine the frequency response of the noise gain are: photodiode parasitics, the input capacitance of the operational amplifier, and RF, CRF, and CF in the amplifier’s feedback loop.

Figure 2. The closing speed of the open-loop gain frequency response and feedback gain frequency response is 20dB/decade.

Figure 2 shows the frequency response of the 1/b curve and the open loop gain response of the amplifier: fP=1/(2w(RPD||RF) (CPD+CCM+CDIFF+CF+CRF)) and fZ+1/( 2w (RF) (CF+CRF)). The AOL (jw) curve intersects the 1/b curve at an interesting point. The closing speed of the two curves indicates the phase margin of the system, so that the stability can be predicted. For example, the closing speed of the two curves is 20dB/decade. Here, the amplifier brings about a phase shift of -90°, and the feedback coefficient brings about a phase shift of 0°. By increasing the 1/b phase shift of the AOL(jw) phase shift, the phase shift of the system can be -90°, and its phase margin is 90°, thus bringing about a stable system. If the closing speed of these two curves is 40dB/decade, it means that the phase shift is -180° and the phase margin is 0°. The circuit will oscillate or ring with the step function input.

One way to correct circuit instability is to add a feedback capacitor CF, or to make the amplifier have a different frequency response or different input capacitance. A conservative calculation method that allows changes in amplifier bandwidth, input capacitance, and feedback resistor values is to place the 1/b pole of the system below half the frequency, and the two curves will intersect at this frequency:

Among them, fGBW is the gain bandwidth product of the amplifier. In this design, the system phase margin is 65°, and the overshoot of the step function is 5%.

The Links: **NL8060BC26-17** **BSM35GD120DN2E3224**