Ltspice Two Stage Op Amp
- Boyle eliminated all but two transistors from his macro- model. The two remaining devices formed the differential-input stage of the op amp; all subsequent.
- REPORT OF RESULTS: Ok, it turned out that the LTspice model I was using for the LM358 op-amp was quite old and was not sophisticated enough to model the frequency response properly. Updating to a relatively recent one by National Semi did not predict the oscillation, but clearly showed the 20% overshoot, which gave me something to work with.
Basic Two Stage CMOS Op Amp This is a common “workhorse” opamp for medium performance applications Provides a nice starting point to discuss various CMOS opamp design issues Starting assumptions: W 1/L 1 = W 2/L 2, W 3/L 3 = W 4/L 4 6 M7 M6 Iref M1.
Introduction
If you haven't already been through the Getting Started with LTSpice guide, you should definitely wait as an update to the audio quality is desperately needed. For those of you who watched it and finished it - bless you. I'd thought I'd kill two birds with one stone here and continue the LTSpice tutorial with an introduction to operational amplifiers -- or op amp for short. We will be covering just the basics here - what are op amps, some common configurations, and a couple examples - and we'll end with a nice, simple project to hopefully get you inspired to work with analog circuits a bit more.
To get started, download the schematics, symbols and simulations by clicking the button below.
Introduction to Operational Amplifiers
An op amp is a voltage amplifying device. With the help of some external components, an op amp, which is an active circuit element, can perform mathematical operations such as addition, subtraction, multiplication, division, differentiation and integration. If we look at a general op amp package (innards to come in a later tutorial) such as the ubiquitous 741, we'll notice a standard 8-pin DIP (dual in-line package):
We are mainly concerned with five of the pins. The circuit symbol for an op amp is a triangle with five pins shown below.
An op amp has a wide range of uses and, depending how each pin is connected, the resulting circuit can be some of the following (this is by no means a comprehensive list):
- Comparator
- An Inverting Amplifier such as a summing amplifier
- A Non-Inverting Amplifier such as a voltage follower
- Difference Amplifier
- Differentiator or Integrator
- Filter
- Peak Detector
- Analog-to-Digital Converter
- Oscillator
Throughout this tutorial I will show you how to measure typical op amp characteristics such as gain, bandwidth, error, slew-rate, current draw, output swing and other characteristics found on device data sheets.
The Ideal Op Amp
The op amp is designed to detect the difference in voltage applied at the input (the plus (v2) and the minus (v1) terminals, or pins 2 and 3 of the op amp package). The difference is also known as the differential input voltage. The output, then, is the difference sensed at the input multiplied by some value A - the open-loop gain. An op amp behaves as a voltage-controlled voltage source, which we will model now. We will simulate both an open-loop and a closed-loop amplifier configuration.
An ideal op amp has the following characteristics:
- Infinite open-loop gain
- Infinite input resistance
- Zero output resistance
- Zero common-mode gain = infinite common mode-rejection
- Infinite bandwidth
- Zero noise
- Zero input offset
Because the input resistance (Rin) is infinite, we can deduce that the current seen at the (+)(v2) and (-)(v1) terminals are zero, using Kirchhoff's laws. Since the output resistance (Rout) is zero, there is no voltage loss at the output. The diamond-shaped voltage source in the image above is known as voltage-dependent voltage source, and in this case the voltage is the gain (G) multiplied by the difference between the input terminals (Vin). The gain is normally referred to as (A) in texts, so the equation for the output is given by:
Let's model a voltage-controlled voltage source and see if we can't get its behavior to mimic an ideal op amp.
Feedback with Amplifiers
Op amps are not meant to be used as stand-alone devices. We simply verified the Vout equation in the ideal op amp video to show why it is commonly referred to as a voltage-controlled voltage source. We are going to talk about feedback and closed-loop gain and application. What is feedback? Feedback occurs when the output of a system is fed back into as input(s). There are two types of feedback: positive (regenerative) and negative (degenerative). Feedback is applied to the system to affect one or more of the following properties:
- Desensitize the gain - the value of the gain becomes less sensitive to variations in the values of the circuit component, such as temperature effects on transistors.
- Reduce non-linear distortion - the output is proportional to the input.
- Reduce the effect of noise - reduces the amount of unwanted electrical interference on the output. This interference could be external or from the circuit components themselves.
- Control the input and output resistances - with an appropriate feedback configuration the input and output resistances can be controlled.
- Extend the bandwidth of the amplifier. We need to be aware of the Gain-Bandwidth Product here. You can extend the bandwidth (to a certain degree) but at the cost of the gain. Gain Bandwidth Product is constant and describes the op amp gain behavior with respect to frequency.
Quick Note about Units
When were talking about gain, we are taking the ratio of the output to the input. If both output and input are expressed in terms of voltage then the units will be Volt/Volt. In the .ac analysis the gain is given in terms of decibels. Here's the conversion formula.
All of the feedback comes at a price, and that cost is the gain. Negative feedback trades gain for more desirable properties; increasing the input resistance also increases the bandwidth.
Closed-Loop Gain
Unlike open-loop gain, the closed-loop gain is dependent on the external circuitry because of the feedback. However, it can be generalized.
Inverting Amplifiers
An example of an inverting configuration consists of one op amp and two resistors, R1 and R2. R2 is connected from the output terminal of the op amp to the inverting or minus terminal of the op amp. R2 closes the loop around the op amp.
How can the answer be improved? Kor son of rynar.
One thing not mentioned in the video below, but is considered implied because we are still using the ideal op amp, is that no current flows through the op amp. All the current (I1) flowing through R1 is also flowing through R2. Another thing to note is that if R1 and R2 are equal in value then this circuit is typically used convert -vout to +vout (changes the phase). This is known as the unity-gain inverter.
Project: The Summing Amplifier
A typical application for an inverting amplifier is a summing amplifier, also known as a virtual earth mixer, used in audio mixing. I happen to have quite a few LM741 op amps lying around, so I went ahead and built a summing amplifier. First I modeled it in LTSpice.
Non-Inverting Amplifiers
The Voltage Follower
The voltage follower is a nice example of a non-inverting amplifier. The property of very high input impedance is a desirable feature of the non-inverting configuration. The voltage follower can used as a unity-gain buffer amplifier connected from a high impedance source to a low impedance source - this helps to avoid loading effects on the driving circuit.
Difference Amplifiers
Difference amplifiers respond to the difference between two signals applied at its input, and rejects signals that are common to the two inputs.
A Single Op Amp Difference Amplifier
Remember that the gain of a non-inverting amplifier is positive and is given by:
and that the gain of an inverting amplifier is negative and is given by:
By combining these two topologies we are getting closer to be able to design a circuit that will be able to obtain the difference between the two input signals. In order to accomplish this, we must first make sure the gain magnitudes (think absolute values that are always positive) of each are equal. By attenuating the gain of the positive path from (1+ R2/R1) to (R2/R1), we've done exactly that. We now have four resistors; we need to make sure the gains are equal so the ratio of the resistors is important:
The problem with this circuit is that in order to obtain high gain, R1 must be relatively low. This causes the input resistance to drop. Another issue is that it isn't easy to vary the gain of this amplifier. Both of these issues are solved with the implementation of the instrumentation amplifier. Using three op amps, we can get a fine-tuned differential amplifier. Since we have the problem of low input resistance using one op amp, we can add an additional voltage follower or buffer at each input. Even more awesome is that the buffers can add to the gain, easing the burden on the difference amplifier in the second stage.
The instrumentation amplifier perfectly combines all the previous material: inverting and non-inverting amplifiers in cascade.
We will not cover integrators, differentiators, oscillators or AD converters in this tutorial. Once we start adding capacitors and inductors, the math gets a bit more specialized and generalized in terms of impedance rather than resistance. These will be a separate tutorial.
Performance Characteristics
If we look at a data sheet for the LM386 audio amplifier, we'll see a ton of parameters that help characterize the op amp. Most of these can be verified with simulation in LTSpice. Before we can get there let's define some of these characteristics.
Common Mode Rejection Ratio
Common mode rejection ratio (CMRR) measures the amount of signal common to both inputs that is not amplified. It is desirable for the common mode gain to be very low, which corresponds with a very high CMRR.
The common mode rejection ratio is the ratio of the absolute value of differential gain to the absolute value of the common mode gain. The differential gain is typically half the intrinsic gain of the MOS transistor set by the manufacturer. Op amps with high output resistance will feature the best CMRR.
Power Supply Rejection Ratio
Power Supply Rejection Ratio or PSRR is the measure of the influence of the power supply ripple on the op amp output voltage. PSSR is important to MOSFET devices as they are usually on mixed-signal ICs where the digital switching in the circuit causes increased power supply ripple. The last thing you want in your design is to have that ripple amplified through your op amp.
The takeaway here is that to minimize the effects of ripple in power supplies, the Op Amp is required to have a large PSRR. So keep that in mind when looking at data sheets for any upcoming projects.
Slew Rate
Slew rate refers to the maximum rate of change possible at the output of an op amp. Most op amps are slew rate-limited, and that is calculated by taking the max of the derivative, with respect to time of the output voltage of the op amp.
Total Harmonic Distortion
The task of an audio amplifier is to take a small signal and amplify it without making any changes other than amplifying it. This is a difficult task because unwanted signals (i.e. ripple) may be amplified along with the desired signal. Any deviation from linearity is considered a distortion. Harmonic distortion is a common form of distortion in audio applications where the peaks of the output signal get 'clipped.' The lower the percentage listed for THD the better, but after a certain point it is hardly perceptible to human ears.
The LM386 Audio Amplifier
Simulate, verify, build – my motto. In this case, the mini portable guitar amp project case, I took it too far. I couldn't find a model I could import into LTSpice and I started from scratch. Below is a button where you can download the project files for what I am about to show you. I designed an op amp based on the LM386, but with MOSFETs instead of BJTs. I actually got this design to slightly out-perform the part I based my design off of, but it only works from 2 to 6 volts. Even though my LM386 model is not exactly like the part used in the project, it is still practical for looking at the electrical characteristics of op amps and getting more familiar with LTSpice.
Project: Mini Portable Guitar Amplifier
I built a small, battery-powered amplifier into the case of my guitar using the LM386 and minimal extra parts. The whole build cost about $5.00 and took less than an hour to put together. The circuit I took directly from the data sheet applications section (Gain of 200):
The only changes I made were to the output capacitor. I didn't have a 250uF capacitor handy to I swapped it out for a 470uF. I also added the 1/4' mono audio female receptacle for the guitar cable and added a status LED so I knew when I was ready to rock. My guitar case has a little cubby for cables and picks so I used that space to build the amplifier into.
Schematic:
Note: J1 is the 1/4' female mono audio jack receptacle.
See it in action:
Resources and Going Further
Ltspice Two Stage Op Amp 4
The Virtual Op Amp Lab:
Music from Outer Space creator Ray Wilson made this MFOS Virtual Operational Amplifier Application, which allows us to experiment with op amps while viewing the output on a simulated oscilloscope.
Music From Outer Space
Ever wanted to get into DIY-synths but don't know where to start? Music From Outer Space is a great resource offering hundreds of schematics designed by Ray Wilson.
Hobbyists
If you are just getting into analog electronics projects, I cannot recommend Forrest Mims' Engineer's Mini Notebooks enough.
Measuring CMRR
EE Times has a fantastic article about common mode rejection ratio and differential amplifiers.
How op-amps work: Part 2 of 2
We left off last time finishing up how the input stage of an op-amp works. The next important stage is made up by transistors Q3,Q5, Q6, Q7, and Q8. The emitters of the differential input (see Part 1) are connected to the emitters of Q5 and Q6, this provides for level shifting, which is required for voltage swing and DC level input at the second stage. The current mirror load is made up of Q3,Q6, R1, and R2. Let’s walk through this a little more.
$$I_{CQ7} = I_{CQ8}$$
Inverting Amplifier Ltspice
$$I = I_{CQ5} = I_{CQ6} = I_{CQ7} = I_{CQ8}$$
$$I_{CQ3} = frac{2 I}{beta} + frac{V_{BEQ8} + I R_{2}}{R_{3}} = frac{2 I}{beta} + frac{V_{T} ln (frac{I}{I_{S}}) + I R_{2}}{R_{3}}$$
Hopefully, these equations shed a little more light on the signal path and general functioning of the 741 op-amp thus far..I assure you, the input stage we completed in Part 1 is the most complicated part of this circuit.
Recall the input stage:
Figure 1
One more feature you may have noticed is the offset null 1 and 2. In simulation this is not necessary to tweak, but in real life it will be necessary to include a pot between offset null 1 and 2. Why? Well, when there is no difference between the two inputs (Q1 and Q2) you may get a nonzero output. This is due to transistor and resistor mismatches..nothing's perfect! To balance the mismatches and obtain a zero output when there is no difference in input, put a pot between offset null 1 and 2 and trim it until your output looks good. To read further on the mathematics about this, Texas Instruments has already worked out some good math about the subject as seen here.
Now this is great and all: we have a pretty solid input stage, things are looking up, we kind of understand what’s going on..But wait! We have a differential input and the 741 op-amp only has one output. How do we convert the differential input to a single ended signal? Whoa, wait a second, what? Oh don’t worry, the creator of the 741 (David Fullagar) already thought this out for us. The active load (Q3,Q8, R1,R2) create a modified Wilson current mirror. Its purpose is to take the differential input current and make it a single-ended signal without the 50% loss of converting from two signals to one. Follow? It gets a little fuzzy, I know. A small signal differential current in Q6 versus Q5 looks summed at the base of Q16. Study the active load schematic closely..It might take some time to absorb this concept, but you'll get it.
Get it? Got it? Good.
Ok, now we finally can move on from that input stage. The single-ended signal is fed to Q16. Q16 and Q15 create a Darlington configuration. That is, the current amplified by the first transistor Q16 is subsequently amplified again by Q15. This creates a high current gain( $$ beta beta $$). Q17 exists as a form of negative feedback to prevent saturation. If it gets too high, Q17 turns on and diverts the base current going into Q16 to ground, thus stabilizing the configuration. This amplifier uses the output side of the current mirror created between Q10 and Q11; it is an active load. Active loads lead to significant voltage gain because if the active load were perfect the voltage gain would be infinite if you worked out the thevenin equivalent resistance for a current source
Figure 2
In figure 2, Q14 provides a voltage level shift. The level shifter stage is included to ensure that there is no DC offset in the output signal. DC offset arises from the turn on voltages of the transistors throughout the circuit. As a exercise run the simulation with and without Q14 noting the differences between the two plots.
Finally we arrive at the output stage! The output stage is composed of Q18, Q20 and Q19. The output stage is a Class AB push pull emitter follower amplifier, go look that up if you're not familiar with the concept. Q18 provides output current limiting much like we saw with Q17. That’s it! Go have fun with the simulation. Play around with it and I think it will all start coming together.
Ltspice Examples
Simulating an inverting amplifier with unity gain (click to enlarge)