Make uninterruptible power supplies for small devices like modems/switches

The circuit of this power supply is shown in the figure below.
1. Charging circuit and its debugging
Initially, influenced by some cheap universal mobile phone chargers, the constant current part was not set (in the dotted box in Figure 1). The two sets of mobile phone batteries are charged in parallel and discharged in series with the help of the contacts K1-1 and K2-1 of relays K1 and K2, so that the voltage reaches the 6V~12V voltage used by the switch. When the external power supply is turned on and the battery voltage does not reach 4.2V, the k-pole of 431 is high impedance, R1, T1, and T2 provide a constant current for the battery, and the external 12V power supply directly supplies power to the switch through Dl. When the battery voltage reaches 4.2V, due to the effect of 431, the battery voltage will no longer increase, and the constant current charging will be converted to constant voltage charging. But in fact, the charging current decreases as the battery voltage increases. When the battery voltage reaches 4.05V, it is difficult to increase it. At this time, the charging current measured by the multimeter is only 30 mA. After analysis, I added the constant current part in the dotted box. Assuming that A4 and R11 are not connected, its working principle is the same as 431. R9 and R10 provide reference voltage for A3. When the voltage of the adjustable resistor R13 is higher than the reference voltage, A3 outputs a low level, otherwise it outputs a high level. After the introduction of R11, due to the positive feedback of R11, A3 can quickly change the output state, and the charging current will not decrease due to the increase of battery voltage, thus greatly improving the charging efficiency.
The debugging method is as follows: first disconnect the battery, connect a 1kΩ resistor to the battery position, and adjust R13 so that A3 just outputs a low level when the battery voltage reaches 4.2V.
Due to the effect of C2, the flip voltage after adjustment is slightly lower than 4.2V, which can avoid overcharging caused by the instability of the adjustable resistor. In order to ensure that the battery voltage does not exceed 4.2V, the voltage of the in-phase input terminal of A3 is set to 2V. Since the circuit cannot automatically recover once it flips, C2 is added to improve the anti-interference ability of the circuit. In order to reliably restore charging after power failure, a diode D2 is also added to the circuit. After power failure, the left side of D2 is not charged, and C2 is no longer charged after being discharged by R13. When power is restored, the voltage on C2 is 0V, the circuit is in a charging state, and C2 is also in a charging state. When the battery voltage does not reach 4.2V, constant current charging continues. When it reaches 4.2V, A3 and A4 output low level, and 431 provides constant voltage charging. A4 is a voltage follower, and its function is to isolate A3 so that it is not interfered by R12.

2. 5V regulated power supply circuit and its debugging
A2 and its peripheral devices constitute a 5V regulated circuit to power the modem. Since the power supply voltage of this part switches between 12V and 7.2V, 431 is used as the reference power supply. Assuming that R7 is not connected, it is a linear voltage regulator circuit. However, due to the positive feedback generated by R7, A3 outputs a low level when the voltage at the inverting input terminal is higher than 5.5V, and outputs a high level when it is lower than 4.1V.
Debugging method: After connecting the circuit, connect a multimeter and a 1kΩ resistor to the +5V output terminal, and adjust R8 so that the multimeter indicates a voltage of 5V. The operating frequency can be changed by adjusting the capacity of C1. The static current of this circuit is about 100mA, which is not too large compared to the modem with a power consumption of 1A. Although its output waveform is not very good, it can be used.
3. Selection of main components
Each battery group consists of two 1050mAh lithium-ion batteries connected in parallel, sharing a protection board. The two battery groups use 4 mobile phone batteries and two protection boards. The power supply uses a commercially available finished switching power supply with an output voltage of 12V and an output current of more than 3A. It can also be replaced by a transformer plus a rectifier filter circuit. The control voltage of the relay is 12V, requiring at least one normally open contact and one normally closed contact, and the contact current is 1A. Due to the incomplete components on hand, 3865 transistors T2 and T3 were selected. In fact, as long as the maximum working current exceeds 1A, the tube will do, but a heat sink must be added. The shell is modified by drilling a four-phase switch box. The circuit has been used in practice and works reliably. It can provide power for two switches and modems for about one hour, which is enough to survive tripping and power outages.