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--- university:courses:electronics:text:chapter-11 [06 Aug 2017 12:37] – Cyril Mechkov
+++ university:courses:electronics:text:chapter-11 [14 Sep 2018 19:59] – spelling correction Daud Zoss
@@ Line 1: / Line 1: @@
 ======Chapter 11: The Current Mirror======
+{{ :university:courses:electronics:text:chptr11-f4.png?500 |}}
 =====11.1 Basic principles=====
-//Basic ideas behind the classic current mirror are revealed below by using the building approach proposed in the Wikibooks story// [[https://en.wikibooks.org/wiki/Circuit_Idea/How_to_Reverse_Current_Direction|How to Reverse Current Direction]].<hidden>The elemental ethics requires, when you use else's ideas, to mention the original source, not to represent them as your own. I have put this issue for consideration in [[https://www.researchgate.net/post/What_is_the_idea_of_the_current_mirror_with_two_emitter_resistors|What is the idea of the current mirror with two emitter resistors]].</hidden>
+The implementation of the current mirror circuit may seem simple but there is a lot going on. The simple two transistor implementation of the current mirror is based on the fundamental relationship that two equal size transistors at the same temperature with the same V<sub>GS</sub> for a MOS or V<sub>BE</sub> for a BJT have the same drain or collector current. To best understand this important circuit building block and how it makes use of this relationship we need to deconstruct the circuit into input and output sections and examine each in turn.
-A current mirror is a circuit block which functions to produce a copy of the current in one active device by replicating the current in a second active device. An important feature of the current mirror is that it has a relatively high output resistance which helps to keep the output current constant, regardless of load conditions. Another feature of the current mirror is that it has a relatively low input resistance which helps to keep the input current constant, regardless of drive conditions. The current being 'copied' can be, and often is, a varying signal current. Conceptually, an ideal current mirror is simply an ideal current amplifier with a gain of -1. The current mirror is often used to provide bias currents and active loads in amplifier stages. Given a current source as the input, we convert the current (entering the current mirror) into a voltage and then use this voltage to control a current sink (the current exiting the mirror); as a result, we obtain a current sink (figure 11.1a). Conversely, given a current sink as the input, we convert the input current (exiting the current mirror) into a voltage and then use this voltage to control a current source (figure 11.1b); as a result, now we obtain a current source. We can generalize this basic current mirror structure in a first conclusion:
+A current mirror is a circuit block which functions to produce a copy of the current flowing into or out of an input terminal by replicating the current in an output terminal. An important feature of the current mirror is a relatively high output resistance which helps to keep the output current constant regardless of load conditions. Another feature of the current mirror is a relatively low input resistance which helps to keep the input current constant regardless of drive conditions. The current being 'copied' can be, and often is, a varying signal current. The current mirror is often used to provide bias currents and active loads in amplifier stages.
-A current mirror consists of a current-to-voltage converter consecutively connected to a voltage-to-current converter.
+The ideal block level concept of the current mirror is shown in figure 11.1. Given a current source as the input, the input section of the current mirror looks like a virtual short circuit and reflects (swaps the direction of flow) this current to produce a current sink (the current exiting the mirror); as a result, we obtain a current sink (figure 11.1a). Conversely, given a current sink as the input, the current mirror reflects this current to control current source (figure 11.1b); as a result, now we obtain a current source. We can generalize this basic current mirror structure with this first observation: A current mirror consists of a low impedance input stage connected to a high impedance output current stage.
 {{ :university:courses:electronics:text:chptr11-f1.png?500 |}}
@@ Line 13: / Line 13: @@
 <WRAP centeralign > Figure 11.1, Current Mirror (a) Sink (b) Source </WRAP>
-It should be noted that the two converters may have a linear relationship (for example where V<sub>OUT</sub> = I<sub>IN</sub>R and I<sub>OUT</sub>= V<sub>IN</sub>/R) like a resistor, but this linear relationship is not required. The converters might be non-linear devices having whatever transfer or I to V characteristics that may even depend on another quantity (such as temperature); the only requirement is the characteristics be the inverse of each other. For example, if the I to V converter implements a function v = f(i) and the other represents the inverse function i = f <sup>-1</sup>(v) the whole function is v = f(i) = f(f <sup>-1</sup>(v)) . So, we can formulate the second conclusion: a current mirror consists of two consecutively connected converters that have inverse transfer functions.
+Conceptually, an ideal current mirror is simply an ideal current amplifier with a gain of -1. In Chapter 8 we explored the transistor and you should recall that the BJT device is a current amplifier of sorts (current controlled current source) in that the collector current is β times the base current. The problem with using this feature directly is that β is not a well controlled value from device to device and can vary with changes in temperature. Accurate current amplifiers are difficult to directly implement using conventional transistor amplifier configurations which are typically voltage amplifiers. For example the MOS transistor is generally modeled as a voltage controlled current source and can not be used directly as a current amplifier. The use of feedback and the current to voltage relationship of two terminal elements such as a resistor are most often used when manipulating currents as signals. Because in a current mirror the input and output are currents, it is easier to convert the input to a voltage first and then convert a voltage back to a current at the output.
+It should be noted that these two stages of the current mirror may have a linear relationship (for example where V<sub>OUT</sub> = I<sub>IN</sub>R and I<sub>OUT</sub> = V<sub>IN</sub>/R) like a resistor. In figure 11.1.1 we see the classic operational amplifier implementation of the current to voltage converter explored back in Chapter 4 section 2. The virtual ground at the negative input of the op-amp provides a very low input resistance. These circuits use the linear relationship between the current in resistor R1 and the voltage across the resistor. However, this linear relationship is not necessarily required. Any element or combination of elements could be used such as the V<sub>BE</sub> or V<sub>GS</sub> of a transistor as in (b) if the output voltage was taken at the gate of M1 (output of the op-amp).
+{{ :university:courses:electronics:text:chptr4-f3.png?600 |}}
+<WRAP centeralign >Figure 11.1.1 Linear Current to Voltage converter (from Chapter 4)</WRAP>
+Similarly, as an output stage we have the operational amplifier implementation of the voltage to current converter from section 1 of Chapter 4 in figure 1.1.2. Here the input voltage is forced across resistor R1 such that the resulting current in R1 flows through transistor M1.
+{{ :university:courses:electronics:text:chptr4-f1.png?600 |}}
+<WRAP centeralign >Figure 11.1.2 Linear Voltage to Current converter (from Chapter 4)</WRAP>
+Implementing the block diagram of the current mirror shown in figure 11.1 follows directly from these voltage / current converter stages from Chapter 4, if we connect the output of the I to V converter in figure 11.1.1(b) to the input of the V to I converter in figure 11.1.2. With the two resistors being equal, I<sub>OUT</sub> would be the mirror image of I<sub>IN</sub>. Note that the second op-amp is not actually necessary because the gates of the two NMOS transistors can be tied directly to each other with the same result. Remember that two equal size transistors at the same temperature with the same V<sub>GS</sub> (or V<sub>BE</sub> for a BJT) have the same drain current. This is an important simplification of the current mirror concept.
+The converters might consist of non-linear devices having whatever I to V characteristics that may include another physical quantity (such as temperature); the only requirement is that the characteristics be the inverse of each other. For example, if the input I to V stage implements a function v = f(i) and the output stage implements the inverse function i = f -1(v) the total input to output transfer function is v = f(i) = f(f -1(v)) . We can make a second observation: A current mirror consists of two connected stages with inverse transfer functions of each other.
+The converter circuits in figures 11.1.1 and 11.1.2 are rather complicated and require as many as two operational amplifiers. A much simpler implementation would be better.
 =====11.2 An input stage to convert current to voltage=====
-We need a configuration where our active element of choice, a transistor, serves as the desired current-to-voltage converter. However, the transistor is a unidirectional device, where for the BJT the base emitter voltage controls the collector current or for the FET the gate source voltage controls the drain current. Producing the opposite where the collector current controls the V<sub>BE</sub> is not possible in the conventional use of the device as a common emitter amplifier. The solution is to incorporate negative feedback. In this case that means making the transistor adjust its base emitter or gate source voltage, V<sub>BE</sub> or V<sub>GS</sub>, so that the collector or drain current is I<sub>IN</sub> = (V<sub>1</sub>-V<sub>BE</sub>)/R. For this purpose, we simply connect the collector to the base or gate to drain. This results in 100% parallel negative feedback (figure 11.2). As a result, with this reversed transistor, the collector current serves as the input quantity while the base-emitter voltage V<sub>BE</sub> serves as the output quantity with a logarithmic transfer function. The input part of the simple BJT current mirror is just a bipolar transistor with 100% parallel negative feedback. Similarly, a diode connected enhancement mode MOS FET (gate tied to drain) will serve as a similar current to voltage converter with V<sub>GS</sub> as the output quantity rather than V<sub>BE</sub>.
+We would like a simple configuration where the active element, a single transistor, serves as the desired current-to-voltage converter. However, the transistor is a unidirectional device, where for the BJT the base emitter voltage controls the collector current or for the FET the gate source voltage controls the drain current. Producing the opposite where the collector current controls the V<sub>BE</sub> is not possible in the conventional use of the device as a common emitter amplifier. Referring back to Figure 11.1.1, the solution is to incorporate negative feedback. In this case that means making the transistor adjust its base emitter or gate source voltage, V<sub>BE</sub> or V<sub>GS</sub>, so that the collector or drain current is I<sub>IN</sub> = (V<sub>1</sub>-V<sub>BE</sub>)/R. For this purpose, we simply connect the collector to the base or gate to drain or "diode connect" the transistor. This classic "diode" connection results in 100% parallel negative feedback (figure 11.2). As a result, with this diode connected transistor, the collector current serves as the input quantity while the base-emitter voltage V<sub>BE</sub> serves as the output quantity with the logarithmic transfer function of the base emitter junction. Similarly, a diode connected enhancement mode MOS FET (gate tied to drain) will serve as a similar current to voltage converter with V<sub>GS</sub> as the output quantity rather than V<sub>BE</sub>.
 {{ :university:courses:electronics:text:chptr11-f2.png?500 |}}
 <WRAP centeralign > Figure 11.2, Current to Voltage Converter </WRAP>
+[[university:courses:alm1k:alm-lab-3|ADALM1000 BJT as a diode lab activity]]\\
+[[university:courses:alm1k:alm-lab-3m|ADALM1000 MOS as a diode lab activity]]\\
+[[university:courses:electronics:electronics-lab-3|ADALM2000 BJT as a diode lab activity]]\\
+[[university:courses:electronics:electronics-lab-3m|ADALM2000 MOS as a diode lab activity]]
 =====11.3 An output stage to convert voltage to current=====
@@ Line 41: / Line 64: @@
 ====11.4.1 Mirror Gain other than 1====
-If transistors Q<sub>1</sub> and Q<sub>2</sub> in figure 11.4 are identical (that is have the same size emitter and thus equal I<sub>S</sub>) the input current to output current ratio or gain is ideally 1. There are often occasions when a gain other than one is required. When building circuits from discreet devices only simple integer ratios are possible while in microelectronic integrated circuits it is possible to make transistors with arbitrary emitter areas, A. However, even in integrated circuits the best design practice is to use identical unit size transistors when making current mirrors.
+If transistors Q<sub>1</sub> and Q<sub>2</sub> in figure 11.4 are identical (that is have the same size emitter and thus equal I<sub>S</sub>) the input current to output current ratio or gain is ideally 1. There are often occasions when a gain other than one is required. When building circuits from discrete devices only simple integer ratios are possible while in microelectronic integrated circuits it is possible to make transistors with arbitrary emitter areas, A. However, even in integrated circuits the best design practice is to use identical unit size transistors when making current mirrors.
 {{ :university:courses:electronics:text:chptr11-f5.png?600 |}}

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