Tips for Current Source Design (I): How to Choose the Right Op Amp

For engineers, current source is an indispensable instrument. Many people also want to make a practical current source. The application of open source kits is just a complete set of PCB, components, programs and other complete products. Participants only need to solder the kit and debug it. How high can the technical content be, and how much technology can we learn from it? This article only starts from the explanation of the principle and guides everyone to make a current source that everyone can control. This article mainly designs the content of the simulation part, and basically does not involve the microcontroller. I hope friends can learn some knowledge from it.

My goal this time is to build a 20V/100mA current source with basic functions, which can have a fixed output and can be controlled by a microcontroller. The figure below is a DC current source that is easy to implement digital control. Assuming that the op amp has ideal output capability, if the output current is 100mA, what are the considerations for the value of the sampling resistor Rsample?

Figure 1

If Rsample is too large, it will result in:

1. The sampling power is too high, which requires high temperature stability of Rsample, so the cost increases exponentially.

Explanation: If Rsample = 1 Ohm, Vsample = 1V, Psample = 100mW, for precision applications, the resistor dissipating 100mW is usually an unacceptable sampling power.

2. The voltage dynamic range on RL is reduced, reducing the upper limit of RL resistance.

However, the requirements for the op amp and Vin conditioning circuit are reduced accordingly.

If Rsample is too small, various errors of the op amp will appear:

1. The drift of VOS is comparable to Vin, causing output current error.

Explanation: Rsample=0.1 Ohm, Vsample=10mV, if using LM324, VOSmax=3mV, potential DC error 30%; VOS/dTmax=30uV/C, 10C temperature change causes potential error 3%.

2. The circuit gain is too high, the op amp noise is amplified, and the voltage on RL remains basically unchanged, causing the voltage noise on RL to increase, resulting in an increase in the current noise on RL.

3. The requirements for op amps increase, so the cost increases linearly.

4. The requirements for the conditioning circuit to process Vin are increased, thus increasing the cost.

But the requirement for Rsample is reduced accordingly.

How to choose the sampling resistor:

The current source needs to sample the current for feedback. Although there are other sampling methods, the most stable and accurate method is still resistor sampling.

Popular knowledge: The resistance power used for sampling should be at least 20 times greater than the sampling power to avoid significant drift due to heat.

Continuing from last time, 100mA current is a very commonly used current value, but it is also usually an awkward current value for resistor sampling.

The current of Class A usually does not require very high accuracy, and shunt sampling is mainly used as long as the power is sufficient.

mA/10mA_级的电流相对简单，由于不产生显著的采样功率，因此通常的精密金属膜电阻都可满足要求。

The current of 100mA level is neither too large nor too small. A shunt does not have such a large resistance, and a precision metal film resistor does not have such a high power.

Figure 2

Solution:

1. Reduce the sampling voltage and use a small resistance

2. Reduce the sampling power. At the same power, the resistance value should be as large as possible.

It seems contradictory, but it is actually very simple, just connect multiple precision metal film resistors in parallel.

Examples:

100mA, 4 sampling resistors, 12 Ohm 0.1% 1/4W 25ppmmax metal film resistors in parallel, equivalent resistance 3 Ohm, sampling voltage 300mV, total sampling power 30mW, power of each resistor 7.5mW.

This approach requires more work on the PCB, keeping in mind that copper also has resistance and that copper itself can act as a temperature sensor.

Usually 0.1% accuracy is not necessary, but temperature drift must be small. However, the accuracy and drift of actual resistor products are basically corresponding, so when buying resistors, you must pay attention to the power in addition to the power.

In addition, it is best for resistors to be aged before leaving the factory. Resistors that have not been aged are usually cheaper, but their performance will change to some extent within a few days after power is applied.

This cost:

12 Ohm 0.1% 1/4W 25ppmmax metal film resistors, priced at 0.50 yuan each for 4 pieces, totaling 2.00 yuan.

Note one of your loads (resistors):

If RL is a pure resistor, it can basically be divided into the following two cases:

1. RL<

2. For some op amps, such as LM1875, a gain of 20 or more is required for stability, which requires RL>=10Rsample.

Otherwise, as shown in the figure below, the slope difference between 1/F and Aopen intersection is 40dB/DEC, and the circuit will oscillate.

In order to ensure sufficient phase margin, the maximum slope difference between the two intersection points is usually required to be 20dB/DEC.

Figure 3

However, a source cannot pick a load unless it exceeds the source's capabilities, for example a voltage source has an output current limit, while a current source has an output voltage limit.

For the first case, it can be eliminated through external compensation of the op amp. Since modern op amps have 0dB stability, it is not the focus of discussion.

For the second case, it is necessary to introduce appropriate frequency compensation in the feedback path. Since the compensation element is usually connected in parallel across RL, it is called an output damper.

For resistive loads, the output snubber, i.e., a capacitor, achieves stability by introducing a zero, z, in the feedback loop, but will limit the feedback system bandwidth.

Figure 4

After compensation, as shown in the figure below, the slope difference between the 1/F and Aopen intersections is 20dB/DEC.

Figure 5

It is very simple to calculate the zero frequency yourself.

The selection of the zero point is based on the Aopen corner frequency of the op amp. To ensure stability under various load resistances, the zero point is usually selected at a lower frequency, sacrificing some frequency response.

Although the second case is rarely used in practice, for example, the current source made of 1875 has serious temperature drift, it can be used as an example of frequency compensation as preparatory knowledge for subsequent use.

This additional cost:

50V withstand voltage 1uF or less CBB capacitor 1 unit price 1.00 yuan, total 1.00 yuan

Total cost: 3.00 yuan

Pay attention to your load 2 (inductance)

Unlike electrical energy generated by chemical and physical methods, power sources that rely on feedback theory have inherent phobias.

Similar to how voltage sources fear capacitive loads, current sources must also be careful when encountering inductive loads.

Off topic: It seems that all voltage stabilizers have capacitors at the output, which conflicts with the above statement. In fact, voltage stabilizers have also been compensated, and the capacitors of the order of 10uF are large enough. The energy of ordinary voltage sources cannot drive 10uF to oscillate at a large amplitude at a specific frequency, but it is not non-oscillating, but the amplitude is very small, which is very similar to ripple. This is why some DIY power supplies in and out of the forum will produce inexplicable "ripples" and "noise".

In addition to resistors and diodes, current sources are more commonly used for inductors, transformers, solenoids, electromagnets, air-core coils, Helmholtz coils, etc. Many inductive loads can reach Class H. Even for small inductors, if the current source is required to have a high response speed, there is the same problem. If there are friends from Tonghui in the forum, you can ask them for advice. A series of current sources from Tonghui are designed for inductor bias current and have a wide frequency response range.

RL is an inductor with DC resistance. (LL+RL) is used as a substitute. (LL+RL) will cause the feedback coefficient F to have a pole pL, and the corresponding 1/F to have a zero, resulting in oscillation. Please calculate the frequency point of pL by yourself.

Figure 6

The solution is compensation. Just introduce a zero point zL on the feedback coefficient F so that a pole appears corresponding to 1/F, and the slope of the 1/F curve at the intersection is 0.

Figure 7

Still, we have done something about the output damper, but it is generally not recommended to use capacitors directly. Although the internal resistance of the inductor is already a damping, it still causes the corrected 1/F curve to be inexplicably near the LC resonance frequency. The usual method is to add a little damping to the capacitor, and connect a small resistor R in series, 1-100 Ohm, depending on the frequency response curve and the value of C in the actual application. Generally speaking, for applications below 10kHz, C=0.1uF, R=3 Ohm/1W.

Figure 8

It's strange why a 1W resistor is used since current usually does not flow through R. Those who have worked on audio amplifiers should have some experience with this, so I won't go into details here.

This additional cost:

3 Ohm/1W cement/carbon film/metal film resistor 1 unit price 0.20 yuan total 0.20 yuan

Total cost: 3.20 yuan

The load problem has been solved, but it seems that the capacitor is still missing. Here is a formula CV=It. Consider it. Current sources are not afraid of capacitors.

No one seems to be interested in these two parts about load, as they are too far away from the soldering iron.

In fact, these are rarely seen in schools and are priorities in engineering.

Analog electronics teachers who have never made anything themselves naturally won’t teach this, which is why school works are usually difficult to turn into products.

Actual op amp:

We have talked so much about the model, but it has not yet touched upon the actual situation. This section will consider the actual devices.

A typical op amp can only output 35mA at most (I've seen it, don't doubt it), and when it reaches the maximum output current, the op amp almost enters saturation and loses most of its remarkable performance.

Of course, the power op amp can output current above 5A, but the DC characteristics of the power op amp are not very good, mainly focusing on VOS and dVOS/dT. Interested forum friends can check the datasheet of LM1875, and the rest are similar.

Since the VOS of the power op amp is comparable to Vsample, it is generally not recommended to use it alone.

Generally speaking, according to the design principles of the op amp itself, the op amp output current should be controlled within 1mA as much as possible, otherwise:

1. Combined with its own bias current, the op amp may heat up and cause output drift.

2. Due to the effect of the collector/emitter series resistance, the high current output causes the op amp output stage to be in poor condition. This is mainly because VCE is too low and IC is too large, resulting in a decrease in current gain. For details, refer to the output characteristic curve in any NPN/PNP datasheet.

3. Increase the intermediate stage load, causing the op amp’s ability to respond to high-frequency large signals to decrease.

For currents greater than 1mA, the current should be expanded.

Fig. 9

There are many ways to expand the flow, the most common methods are as follows:

1. Use an off-the-shelf unity-gain buffer:

For example, LT1010 has a maximum output of 150mA.

2. Refer to the internal circuit of the op amp:

The simplest way to expand the current is to use a common collector class B push-pull output stage, which is an emitter follower combination consisting of NPN and PNP. For 20V/100mA, a medium power tube of about 10W must be selected. In fact, it is a simplified method of the first method.

3. Use a power amplifier circuit with voltage gain to expand current:

This is a luxurious method with quite good dynamic performance. Many Agilent advanced system instruments adopt this method. Of course, the power amplifier is discrete. Since the current expansion circuit has voltage gain, the SR requirement of the amplifier is reduced. The DC performance of the overall circuit is determined by the amplifier, which overcomes the VOS problem of the power amplifier. However, this circuit is more troublesome to debug and is prone to oscillation, requiring the designer to be experienced.

Obviously, considering the cost performance, if the current source is only considered as a stable drive without considering the dynamic performance (such as pulse current source), the second method is a very good choice.

Someone must have recommended that it is best to use Class AB output to avoid crossover distortion, which is also possible, but it is not necessary for a DC source.

Fig.10

The above circuits can work in quadrants I, II, III, and IV. For general purposes, there are actually very few occasions where a current source that can work in all four quadrants is required. Usually, only quadrant I is required (Io>0, Vo>0). If dynamic performance is not considered, the PNP side of the push-pull output stage can be removed to simplify it to a single-arm output.

This simplification sacrifices the output current falling edge performance, but it does not affect the DC stable source.

Forum members can refer to the Agilent 36xx series user manual for the huge difference in falling edge and rising edge response rates. 36xx are all single-arm power supplies.

Fig.11

The op amp in the figure uses dual power supplies. The op amp can work with a single power supply or dual power supplies. It is recommended to use dual power supplies for the following reasons:

1. Aopen (Vin+-Vin-) = Vo is the basic formula of op amp. It is usually believed that Aopen is infinite, but the actual op amp is no more than 140dB (icl7650), and some op amps are even only a few thousand (TL061).

Transforming the formula, we get (Vin+-Vin-)=Vo/Aopen. Remember that all voltages are referenced to the midpoint of the dual power supply. (Vin+-Vin-) is the error of the op amp.

When working with a single power supply, the error can be minimized when Vo=1/2Vcc. When working with dual power supplies, the error is lowest when Vo=1/2(Vcc-Vee)=0. Relatively speaking, the latter is easier to grasp. This problem will be solved with practical application methods later.

2. Even rail-to-rail op amps cannot achieve absolute rail input/output, so there will be some annoying problems when the input/output needs to be 0. Using dual power supplies can avoid these problems and focus on the key points.

Some problems still exist :

The circuit is basically formed, are there any other problems?

Generally speaking, the design work can be completed at this point. However, a careful analysis shows that there are still some imperfections.

Popular knowledge: Current source and voltage source are complementary. First, let's look at the voltage source:

1. Sensitive to capacitive loads, but not so sensitive to inductance.

2. There is a maximum current limit. When short-circuited, the output current is limited by the current capability of the voltage source.

3. The load is connected in parallel between the output terminal and ground.

Corresponding to the current source:

1. Sensitive to inductive loads, but not to capacitive loads

2. There is a maximum voltage limit. When the circuit is open, the output voltage is limited by the voltage capability of the power supply of the current source.

3. 。。。

The third point is a problem. The load of the obtained current source is connected between the output terminal and the sampling resistor, and participates in the feedback, thus causing the following problem.

1. Load Regulation

Imagine that the load ranges from 0-100 Ohm, and the voltage at the output of the op amp needs to vary between 1 and 10V. According to the previous op amp error analysis, the (Vin+-Vin-) corresponding to 10V and 1V differs by 10 times. If the op amp is TL061 (Aopen=6000), the input error varies between 1V/6000 and 10V/6000, that is, 0.16mV-1.6mV, corresponding to Vsample=300mV, and the current error is 0.05%-0.5%, so the load regulation rate in the range of 0-100 Ohm is 0.45%, which is considerable. The load regulation rate of ordinary commercial power supplies will not exceed 0.01%.

Of course, if you change to a better op amp, such as OP07 (gain 1000000), it will be much better, with a load regulation rate of 0.003%, which can basically be ignored.

However, if you can use it better, try to use it better. Even if it is a cheap OP07, try to give full play to its proper indicators.

Why do we blindly pursue load regulation rate? In fact, the load regulation rate corresponds to the parallel internal resistance of the current source. The smaller the load regulation rate, the higher the parallel internal resistance, the smaller the shunt, and the better the current source performance.

Corresponding to the voltage source, the load regulation rate corresponds to the series internal resistance of the voltage source. The smaller the load regulation rate, the smaller the series internal resistance, the smaller the voltage division, and the better the voltage source performance.

2. The output voltage cannot reach 20V

To be honest, the reason why I chose 20V in the question is to explain the problem here. Most op amps have a maximum recommended supply voltage of +/-15V when using dual power supplies. Of course, there is also the OP07 (limit +/-22V) family that can reach +/-20V.

Even if OP07 is used, the maximum output voltage is only +/-18V when working at +/-20V. Therefore, the E of NPN, that is, the maximum voltage at the output of the current source is 17.4V. Taking Vsample=300mV into account, the output voltage that the current source can achieve is 17.1V. Moreover, the current gain of medium-power NPN is only a few dozen, so Darlington configuration must be used to reduce the op amp load, which will remove 0.6V and compress the maximum output voltage to 16.5V.

Of course, there are suggestions to use an asymmetric dual power supply, such as +30V -5V, which can make the output voltage reach more than 20V.

This configuration is acceptable if necessary, but for the following reasons:

(1) If the Vin+ terminal voltage is very close to 0V, the op amp input stage transistor will work in an uncomfortable state. VCE is too small, resulting in a decrease in current gain, causing the op amp Aopen to decrease and the input bias current to increase.

(2) A decrease in Aopen will also cause a decrease in the load regulation rate indicator.

Generally, it is not recommended to use asymmetric dual power supplies with large differences. Single power supply is the extreme of asymmetric dual power supply, so the performance will be greatly discounted compared with dual power supply. This is why single power supply is not recommended for early op amps. However, the emergence of handheld devices has greatly promoted the application of single power supply. Modern single power supply op amps have made great improvements, such as rail-to-rail, but the price is also much higher. Without losing other performance, the price is usually several times that of ordinary op amps.

The current source architecture cannot completely solve the above problems and the architecture must be changed.

By utilizing the mirror principle of the transistor (IB is approximately equal to 0, IC=IE), the load can be removed from the feedback loop and moved between the power supply and C, thus achieving the correspondence with the voltage source: "the load is connected in series between the output end and the power supply."

Fig.12

At this time, the voltage at the output of the op amp is basically controlled between 0.6 and 0.9V. Even the TL061 can reach 0.016%, and the OP07 can reach 0.0001%.

If the op amp power supply VCC is separated from the power supply VP connected to the load, and the power supply VP connected to the load is 24V, the output voltage of the current source can reach more than 20V.

However, the current gain of the transistor is limited after all. Even the Darlington configuration is only 1000, and the maximum of the super beta transistor (usually used in the input of bipolar op amps) is no more than 10000. IB will always appear, and IB flows into the ground through Rsample, causing errors in Vsample. The error is 1/current gain.

NS has a circuit that avoids this problem, using JFET and NPN to form a Darlington configuration that does not require current drive.

Fig.13

However, low-power JFET or N MOS is not cheap, while power N MOSFET is not expensive and can also reduce one type of inventory, so N MOSFET can be used instead of NPN.

Fig.14

MOSFET does not require stable current drive, so the Vsample error caused by IG can be basically ignored, ID=IS, a nearly perfect mirror image.

N-MOSFET of around 10W is not cheap, so it is wise to choose 100W IRF530, which also provides potential for expanding output power.

This additional cost:

IRF530 1 piece unit price 3.00 yuan, total 3.00 yuan

Total cost : 6.20 yuan

How to choose the right op amp:

The choice of op amp depends on the needs. Each op amp has a suitable use and is not universal.

Current source requirements:

1. Vin+=Vin-=Vsample, Vsample=300mV. Under any constant temperature and normal working conditions, the error source Vin+-Vin- should be less than 0.01% of Vsample=30uV.

2. The smaller the VOS caused by temperature change = Vin+-Vin-, the better. Precision instruments require an ambient temperature range of 25+/-10C==15-35C, so the VOS change within the +/-10C range should be less than 0.01% of Vsample=30uV.

3. For stable current output, the step response requirements can be appropriately relaxed without considering pulse performance.

4. Low noise.

5. The lower the price, the better.

This is the way of thinking in engineering, with the scope ranging from wide to narrow:

1. The previous calculation of load regulation shows that the larger Aopen is, the smaller Vin+-Vin- is. A very high Aopen is a typical feature of precision op amps. Usually Aopen>120dB=1000000. The available op amps are:

OP07 family, including OP07/27/37/177/A277/227.

Common op amps such as LM358/324, TL061/071/081, LF356/357/347, etc. are not precision op amps and are not used for the time being.

2. The VOS of precision op amps is usually very small, less than 1mV, and VOS/dT is also very small, less than 2uV/C. Taking OP07 as an example, VOS/dTmax=1.6uV/C, +/-10C changes by +/-16uV, which meets the requirements.

One might ask: why not use the typical value of VOS/dT for calculation (even the LM324 is very small), but use the maximum value?

Fig.15

The principle of engineering design is redundancy. When doing a project, you must leave enough redundancy. Those that do not leave redundancy are usually school works or works by novice. When doing a project, you cannot gamble and you must try to consider the worst case scenario. The redundancy happens to be the maximum value.

Theoretically, the measurement circuit of VOS/dT is different from the actual application circuit, so the typical value can only be used as a reference, not a standard. When choosing an op amp, you must look at the widest range of the indicator. In fact, the maximum value can only be used as a reference, but since there is no data support for other circuit forms (in fact, it is not operable), only the maximum value can be used as the basis for calculation.

There is nothing wrong with the OP07 family. High Aopen and low VOS and VOS/dT always appear together, just like high accuracy and low temperature drift of resistors always appear together.

The single op amps of the OP07 family have the added benefit of being zero-adjustable.

3. When the quality of the rising edge of the step response is not considered, the op amp does not need to have a large gain at high frequencies. For a stable source, the op amp GBW is about 1MHz. The IRF530 behind the op amp is also not a high-frequency device, so it is a waste to choose an op amp with a large GBW, and future frequency compensation will be quite troublesome. Of course, if the current source is required to work in a pulse state (a method that many semiconductor measurement systems must use to avoid heating), the op amp and MOSFET can be replaced accordingly.

The OP27/37 in the OP07 family are both broadband, so they are not considered for now. (The specifications are too high, very good op amps, and the OP37 is simply a masterpiece)

OP07/177/OPA277 are all op amps with a frequency of around 1MHz.

4. The noise of OP07 family is low enough.

5. This question is always tricky, but OP07 is very suitable, good quality and low price. 177 is also very good, not too expensive, OPA277 is more expensive, but VOS/dT is very low, keep it as an alternative.

There is also a kind of precision operational amplifier such as ICL7650, which is called chopper amp.

There is some noise, but not much, and the better chopper amps will quantize the low frequency noise into high frequencies through sampling, which can be easily filtered out.

Aopen is very high > 140dB, and the power supply range is slightly smaller, +/-8V. Since the current source architecture does not require the op amp output to be dynamic, it is also acceptable.

The most important VOS/dT is theoretically 0, but in reality it is a long-term drift caused by the long-term performance inconsistency of the switch.

But once this type of op amp is saturated, it is difficult to recover quickly, which is a major disadvantage. And it is very expensive.

OP07CP is the temporary choice. There are always too many choices for op amps, which is dazzling. Therefore, most designers always use the most familiar models instead of seeking new ones.

Since there is only one op amp in the current source, the zero drift comes from the op amp, which is exactly the most suitable application occasion for the OP07 zero adjustment circuit.

See the OP07 datasheet for the zero adjustment circuit. Appropriate improvements need to be made to split the 20k potentiometer into 9.1k+2k potentiometer+9.1k to improve the adjustment accuracy.

Fig.16

This additional cost

OP07CP 1 piece unit price 1.20 yuan, total 1.20 yuan

9.1k Ohm resistor 2 pieces, unit price 0.01 yuan, total 0.02 yuan

2k Bouns 10-turn precision fine-tuning 3296 potentiometer, unit price 2.00 yuan, total 2.00 yuan.

Total 3.22 yuan

Total cost: 9.42 yuan

How to solve the oscillation problem:

I believe that no one has tried it yet, and it would be best if they have built the circuit mentioned above. However, they found that it did not work at all, either it vibrated when it was turned on, or it started to vibrate when the current was large.

I am totally confused, the feedback seems to be negative feedback, and there is basically no vibration when using NPN. It is very strange and very angry, because I have no solution and no idea.

This is an inherent problem with negative feedback. Any negative feedback has the opportunity to oscillate as long as the phase is wrong.

However, there is another saying: all negative feedback oscillation problems can be solved. Take a reassurance first.

Solving the oscillation problem is the process of tailoring the frequency response curve. Therefore, the frequency response of the open-loop gain Aopen and the feedback factor F must be obtained first.

The feedback factor F is 1, which is the 0dB line on the Bode plot.

The open-loop gain Aopen is a little more complicated. Based on the circuit on the 39th floor, first draw the small signal equivalent circuit.

The open loop is divided into three parts:

1. Op amp

2. MOSFET input

3. MOSFET output

Fig.17

The transfer function of this circuit is not easy to calculate because Cgs is not grounded and is coupled with the voltage-controlled current source gmVgs. When I was teaching a graduation project at school, I once asked a student to solve it once, but he didn't know how many triangles there are in the diode symbol. He was very rigorous and dedicated. He not only solved it but also checked it three times. It was a waste to give it to the school for training.

The transfer function is calculated to be a Laplace transform of one inch high and two inches wide. I really don't have time to deduce it again, but if we ignore some unimportant quantities, since Rsample is very small, the difference with Cgs grounding is not much.

Fig.18

Ro after the op amp is the output resistance of the op amp, that is, the current limiting resistance of the op amp output stage, which is roughly around 200 Ohm. It can be roughly deduced by the following method:

The critical saturation output voltage of the non-regular rail-to-rail op amp is Vcc-4V, the maximum output current is about 20mA, and the current limiting resistor is about 200 Ohm.

Cgs is more complicated. According to the description on the datasheet, Ciss=760pF@Vgs=0/VDS=25V, but the decrease of VDS and the increase of Vgs will increase Ciss to about 1000pF.

Fig.19

At the same time, the transconductance capacitance Crss is omitted in the figure. Crss can be equivalent to the small capacitance at the input and output ends through Miller's theorem, which is very small and can be ignored.

gm is a problem. Although we can find the DC gm, which is roughly 7@Id=8A/VDS=50V, it is actually used at Id=100mA/VDS<20V. According to the output characteristic curve in the datasheet, we can see that in the saturation region, gm decreases as Id decreases, and has little to do with VDS. In the variable resistance region, gm decreases significantly as Id and VDS decrease. When Id is very small, gm is roughly around 1-3. Temporarily take 2.

Fig. 20

gm also has a transition frequency, which eventually produces fT, but this parameter is difficult to obtain because most power MOSFETs are used in switching states, and gmDC varies greatly with bias, so it is usually not given in the datasheet. However, from the on-time, Ciss, Coss, and Crss, it can be roughly inferred that gm's fT is very high, and divided by gmDC is the transition frequency, which is very high, roughly around 10MHz. This is far beyond the operating range of OP07, so it is ignored and gm is considered to be a horizontal straight line that does not change with frequency.

It can also be seen why OP37 was not used before, because the corner frequency of gm is just within the operating frequency range of OP37, which increases the complexity of frequency compensation.

Analysis of Aopen 1: The dominant pole of the op amp

The op amp is a multi-zero-pole system, but generally has two main poles, a low-frequency main pole close to DC and a high-frequency main pole close to GBW. The figure shows the open-loop gain frequency response curve of OP07.

Fig.21

Of the two main poles, the high-frequency main pole is usually not taken seriously because the high-frequency main pole of most op amps is below the 0dB line, that is, unity gain stable. When there is only one op amp in the feedback loop, it is rare to encounter a gain less than 1. Therefore, the high-frequency main pole is not marked in many op amp datasheets.

Considering the op amp cascaded with a 10x ideal gain stage (which is sometimes necessary), this high frequency dominant pole will surface, and if the closed-loop gain is 1, oscillation will occur.

Fig. 22

Fig.23

Analysis of Aopen Part 2: MOSFET and Rsample

As mentioned before, the MOSFET is divided into two parts, input and output. By reasonable simplification, the Cgs of the input is grounded.

We should be grateful for the design method of input and output power isolation. I don’t know who invented the electron tube first, otherwise this part of the analysis would be quite complicated.

1. Input part

The input part is composed of Ro = 200 Ohm and Cgs = 1000pF, which forms a low-pass filter and generates a pole po. The low-frequency gain is 0dB, and the pole po that generates the corner frequency is located at about 800kHz. It just falls within the frequency band above 0dB of OP07, so it is speculated that it is related to oscillation.

Fig.24

2. Output

The MOSFET current Id=gmVgs flows through Rsample to generate a voltage gmVgsRsample, so the gain is gmRsample. Since the turning frequency of gm is very high, Rsample is an ideal resistor at low frequencies, so the frequency response of gmRsample is a straight line parallel to the 0dB line.

When the current source output current is very small, gm is close to 0, so gmRsample is very low below the 0dB line. The increase in output current causes gm to increase, and gmRsample continues to move up until the maximum current is reached, gm=2s, Rsample=3 Ohm, gmRsample=6, and moves above the 0dB line.

Fig.25

After the two parts are cascaded, the gains are multiplied and the gains are added on the Bode plot, as shown below:

Fig.26

At this time, if gmRsample>1, the pole po is above the 0dB line, otherwise it is below the 0dB line.

Once po is higher than the 0dB line, and 1/F=1 (0dB) and the op amp's own Aopen has a slope of -20dB/DEC near this frequency, the slope will reach -40dB/DEC after po, and oscillation may occur.

Therefore, it can be inferred that the generation of oscillation should be related to Ro, Cgs, gm and Rsample.

Analysis of Aopen Part 3: Why does it oscillate?

Cascading the transfer function composed of the op amp, MOSFET and Rsample, we get the complete open-loop gain Aopen shown in the figure below:

Fig. 27

Aopen has three main poles, namely:

1. Op amp low frequency dominant pole pL

2. Pole po caused by MOSFET input capacitance

3. pH of the high frequency main pole of the op amp

When gmRsample < 1, po is below the 0dB line and the system is stable.

When gmRsample>1, po is above the 0dB line and the system oscillates.

When gmRsample=1, po=0dB, and the system is in a critical state.

The reason for this problem is simple:

gm is closely related to the current Id. As Id increases, gm increases. Therefore, gmRsample

It may change from "1" to "1", so that the pole po is above the 0dB line, and the 1/F=0dB line is

The slope difference at the intersection of Aopen is 40dB/DEC, so the system oscillates.

Of course, oscillation can be avoided by reducing Rsample, but this is not a permanent solution and will cause a series of problems such as cost and noise.

A basic principle when dealing with oscillation is to try to trim Aopen first, and then 1/F. Changing 1/F may cause changes in the transient performance of the system.

Frequency compensation is a double-edged sword that may cause system performance degradation, and excessive single compensation will cause a lot of problems. Therefore, multiple compensation methods should be used as much as possible, and each compensation should be used in moderation.

This time, three compensation methods will be used to solve three problems respectively:

1. Acceleration compensation

2. Noise gain compensation

3. High frequency integral compensation

Due to space constraints, I will stop here for the first part. Next, I will talk about acceleration compensation and Aopen correction issues, so please pay attention.