**What is Current Mirror? – Circuit Diagram and its Workings**

The **two-transistor current source**, also called a **current mirror**, is the basic building block in the design of integrated circuit current sources. Figure 20.25 (a) depicts the basic current-source circuit, which consists of two matched or identical transistors Q_{1} and Q_{2}, operating at the same temperature, with their base terminals and emitter terminals connected together. The base-emitter voltage, V_{BE} is, therefore, the same in the two transistors. Transistor Q_{1} is connected as a diode; consequently, when the supply voltage is applied, the base-emitter junction of transistor Q_{1} is forward biased and a reference current I_{REF }is established.

Although there is a specific relationship between I_{REF} and V_{BE1}, V_{BE1}Â can be thought of as the result of I_{REF}. Once V_{BE1}Â is established, it is applied to the base-emitter junction of transistor Q_{2}. The applied V_{BE2} turns Q_{2}Â on and generates the output current, which is employed to bias a transistor or transistor circuit.

The reference current in the two-transistor current source can be established by connecting a resistor to the supply source +V_{CC}Â as shown in Fig. 20.25 (b). The reference current is then

where V_{BE} is the base-emitter voltage corresponding to collector current (I_{REF}).

Connecting the base and collector terminals of a BJT effectively provides a two-terminal device with ampere-volt characteristics that are identical to the i_{C }versus v_{BE}Â characteristic of the BJT.

**Current Relationships:** Figure 20.25 (a) depicts the current in the two-transistor current source. Since V_{BE} is the same in both devices, and the transistors are identical, then I_{B1}Â = I_{B2}Â and I_{C1}Â = I_{C2}. Transistor Q_{2} is assumed to be biased in the forward-active region. Applying Kirchhoff’s current law to the collector node of transistor Q_{1}, we have

Replacing I_{C1} by I_{C2} (i.e., I_{C1 }= I_{C2}) and noting that I_{B2}Â = I_{C2}/Î², above equation becomes

i.e., the constant current provided at the collector of transistor Q_{2} mirrors that of transistor Q_{1}

Since

The current I_{REF}Â set by V_{CC} and R_{1} is mirrored in the current into the collector of transistor Q_{2}.

Transistor Q_{1} is referred to as a diode-connected transistor because its base and collector are shorted together.

**The operation of the current mirror may be described as follows:**

- Q
_{1}acts like a diode and a current is established through it. - Q
_{1}will develop a voltage drop V_{BE}, in response to the current. - The base-emitter of Q
_{2}is in parallel with that of Q_{1Â }(V_{BE1}Â = V_{BE2}Â = V_{BE}). - Q
_{2}‘s collector current will be established in response to its V_{BE}. - Since the two transistors are matched, Q
_{2}‘s collector current will be approximately equal to Q_{1}‘s collector current. Q_{2}‘s collector current is said to “mirror” the current through Q_{1}.

Q_{1} is often called a **compensating diode** because it automatically compensates for variations in temperature. Matching of diode curve means matching at all temperatures as well as voltages. When the temperature increases, the voltage across the emitter diode falls approximately 2 mV per degree. Since the voltage across the compensating diode also decreases by 2 mV per degree, the collector current is little affected with temperature increase.

**Modified Current Mirror:**

Equation (20.48) reveals that the collector current in the transistor Q_{2} is related to the reference current I_{REF} by a factor (Î²+2/Î²). For Î² >> 2, I_{C2}Â = I_{REF1}, but for low-current transistors I_{C2} can differ significantly from I_{REF}. However, this error can be reduced by introducing another transistor as an emitter follower. The resulting circuit, as shown in Fig. 20.26, is a modified current mirror circuit or **three-transistor current source**. We again assume that all transistors are identical; therefore, since the V_{BE} is the same for transistors Q_{1} and Q_{2}, I_{B1} = I_{B2} and I_{C1} = I_{C2}. Transistor Q_{3 }supplies the base currents to Q_{1} and Q_{2}, so these base currents should be less dependent on the reference current. Also, since the current in transistor Q_{3} is substantially smaller than that in either Q_{1} or Q_{2}, the current gain of Q_{3} is expected to be less than those of transistors Q_{1} and Q_{2}. We may define the current gains of transistors Q_{1} and Q_{2} as Î²_{1}Â = Î²_{2}Â = Î²,Â and current gain of the transistor Q_{3} as Î²_{3}.

Applying Kirchhoff’s current law to the collector node of transistor Q_{1}, we have

Combining above Eqs. (20.49), (20.50) and (20.51), we have

Replacing I_{C1} by I_{C2} and noting that I_{B2}Â = I_{C2}/Î², the above Eq. (20.52) may be rewritten as

The output or bias current is then

The reference current is given by

As a first approximation base-emitter voltages of transistors Q_{1} and Q_{3} are assumed to be equal (i.e. V_{BE3}Â = V_{BE1}) as indicated in Eq. (20.55).

A comparison of Eq. (20.54) for the three-transistor current source and Eq. (20.48) for the two-transistor current source reveals that the approximation of I_{out}Â â‰¡ I_{REF}Â is better for three-transistor circuit.

**Note :** For a two-transistor current source (Fig. 20.25) and for a three-transistor current source (Fig. 20.26), a large valued resistor R_{1} is required for a small biasing current, which is not feasible because it becomes costly in terms of chip area. Usually, these current sources are employed for producing a current of about 0.3 mA-0.5 mA.

**Multiple Current Source:**

In the previous current sources, we established a reference current I_{REF}Â and one load current I_{out}. In the two-transistor current source in Fig. 20.25 (a), the base-emitter junction of the diode-connected transistor Q_{1} is forward biased, when the bias voltage +V_{CC} is applied. Once V_{BE} is established, the voltage is applied to the base-emitter junction of transistor Q_{2}, which turns Q_{2} on and generates the output current I_{out}. The base-emitter voltage of transistor Q_{1} can also be applied to additional transistors, to generate multiple load currents. Consider the circuit shown in Fig. 20.27. Transistor Q_{R}, which is the reference transistor, is connected as a diode. The resulting base-emitter voltage of reference transistor Q_{R}, established by reference current I_{REF}, is applied to N output transistors, producing N load currents.

The relationship between each load current and the reference current, assuming all transistors are matched, is

The collectors of multiple output transistors can be connected together, changing the load current versus reference current relationship. For an example, the circuit depicted in Fig. 20.28 has three output transistors with common collectors and a load current I_{out}.Â Assuming that transistors Q_{R}, Q_{1}, Q_{2 }and Q_{3} are all matched if the current gain Î² is very large, the base currents can be neglected and I_{1}Â = I_{2} = I_{3} = I_{REF},Â and the output current l_{out} = 3I_{REF}. This process is not recommended for discrete devices, since a mismatch between devices will usually cause one device to carry more current than the other devices. Connecting transistors in parallel increases the effective base-emitter area of the device. In actual IC fabrication, the base-emitter area would be doubled or tripled to provide an output current twice or three times the value of I_{REF}.

**Wilson Current Source:**

This is another configuration of a three-transistor current source, known as a **Wilson current source**. The circuit is shown in Fig. 20.29. This circuit has a large output resistance. We again assume that all the transistors are identical, with I_{B1}Â = I_{B2}Â = I_{B}; I_{C1}Â = I_{C2}Â and V_{BE1}Â = V_{BE2}.

Applying KCL at the emitter of transistor Q_{3}, we have

Comparing Eqs. (20.57) and (20.58), we have

Applying KCL at the collector of transistor Q_{1}

The difference

is extremely small error for modest values of Î².

In the Wilson current source, the output resistance looking into the collector of Q_{3}Â is R_{outÂ }â‰¡ Î²r_{03}/2, which is approximately a factor Î²/2 larger than that of either the two-transistor source or the basic three-transistor source. This means that, in the Wilson current source the change in bias current I_{out} with a change in output collector voltage is much smaller.

**Widlar Current Source:**

The basic current mirror shown in Fig. 20.25 (b) has a limitation that for low value current source the resistance R_{1} required is sufficiently large and cannot be fabricated economically in IC circuit. For a two-transistor current shown in Fig. 20.25 (b), if a load current of I_{out}Â = 10Î¼AÂ is required, then for V_{CC} = 10 V, the required resistance value is

The solution to above problem is a circuit shown in Fig. 20.30, called a **Widlar current source**. This circuit isÂ particularly suitable for low value of current. The circuit differs from the basic current mirror [Fig. 20.25 (b)] only in the resistance R_{E} that is included in the emitter lead of transistor Q_{2}. A voltage difference is caused across emitter resistor R_{E1} so that the V_{BE2} is lesser than V_{BE1}. A smaller V_{BE} produces a smaller collector current. It means that the load current I_{out} is lesser than reference current I_{REF}.

For Î² >> 1 for transistors Q_{1} and Q_{2} and for transistors to be identical

Subtracting Eq. (20.67) from Eq. (20.66), we have

From the circuit, we see that

Comparing Eqs. (20.68) and (20.69), we have

Equation (20.70) provides the relationship between the reference and bias currents. Sometimes, emitter resistances are used in both the transistors Q_{1} and Q_{2} as depicted in Fig. 20.31.

From the circuit shown in Fig. 20.31.

Applying KVL in the base-emitter loop, we have

Comparing Eqs. (20.72) and (20.73), we have

For the range 0.1 < I_{C2}/I_{C1}Â < 10 it can be assumed that I_{C2}/I_{C1}Â â‰¡ R_{E1}/R_{E2}. Thus even large ratio is obtained by the modified circuit (Fig. 20.31).