Table of Contents
Understanding BJT Current Mirrors
A current mirror is a circuit designed to copy a current through one active device by controlling the current in another active device of a circuit, keeping the output current constant regardless of loading. These fundamental building blocks are essential in analog integrated circuit design, serving critical roles in biasing networks, active loads, and current regulation applications.
The simplest bipolar current mirror implements this idea and consists of two cascaded transistor stages acting accordingly as a reversed and direct voltage-to-current converters. The basic configuration typically involves two matched transistors, with one transistor establishing the reference current and the other mirroring it. 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 VBE for a BJT have the same drain or collector current.
The operating principle relies on the exponential relationship between base-emitter voltage and collector current in bipolar junction transistors. The emitter of transistor Q1 is connected to ground, its collector and base are tied together, so its collector-base voltage is zero, and consequently, the voltage drop across Q1 is VBE, that is, this voltage is set by the diode law and Q1 is said to be diode connected. This diode-connected configuration creates a logarithmic current-to-voltage converter that sets the base voltage for the output transistor.
Fundamental Design Principles
Transistor Matching Requirements
It is important to have Q1 in the circuit instead of a simple diode, because Q1 sets VBE for transistor Q2. If Q1 and Q2 are matched, that is, have substantially the same device properties, and if the mirror output voltage is chosen so the collector-base voltage of Q2 is also zero, then the VBE-value set by Q1 results in an emitter current in the matched Q2 that is the same as the emitter current in Q1.
Because temperature is a factor in the “diode equation,” and we want the two PN junctions to behave identically under all operating conditions, we should maintain the two transistors at exactly the same temperature. This is easily done using discrete components by gluing the two-transistor cases back-to-back. If the transistors are manufactured together on a single chip of silicon (as a so-called integrated circuit, or IC), the designers should locate the two transistors close to one another to facilitate heat transfer between them.
For the above applications, it is recommended to use dual BJTs (two BJTs assembled in a single package). This ensures that the temperature of both dies will be almost identical because the two transistors are physically adjacent to each other. In additional, using matched devices guarantees that the electrical parameters of the transistor pair are almost identical, ensuring almost perfectly symmetrical behavior.
Current Scaling and Gain
If transistors Q1 and Q2 in figure 11.4 are identical (that is have the same size emitter and thus equal IS) 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.
If Q2 and Q3 are equal-area transistors the load currents Iload will be equal. If we need a 2·Iload, parallel Q2 and Q3. Better yet fabricate one transistor, say Q3 with twice the area of Q2. Current I3 will then be twice I2. In other words, load current scales with the transistor area. This scaling capability makes current mirrors extremely versatile for generating multiple bias currents from a single reference.
Step-by-Step Calculation Process
Determining Reference Current
The design process begins with selecting the reference current based on circuit requirements. The reference current is typically established using a resistor connected between the supply voltage and the diode-connected transistor. For a basic current mirror, the reference resistor value is calculated using the fundamental relationship:
RREF = (VCC – VBE) / IREF
Where VCC is the supply voltage, VBE is the base-emitter voltage (typically 0.6-0.7V for silicon BJTs), and IREF is the desired reference current.
Practical Design Example
Let us design a practical current mirror for 1mA output current from a 12V supply. Set Iref = Iout = 1mA (for a 1:1 mirror). We want Iref to flow through Rref from VCC. Rref = (VCC – VBE) / Iref = (12 – 0.7) / 0.001 = 11.3V / 1mA = 11.3 kΩ
Use the nearest standard value: 11kΩ (giving Iref = 1.027mA). The 10kΩ in E12 series gives 1.13mA — acceptable for most applications. This demonstrates the practical approach of using standard resistor values and accepting small deviations from the ideal design values.
Transistor Selection Criteria
For a 1mA current mirror, almost any small-signal NPN transistor works. Key requirements: VCEO ≥ VCC (12V in this example) — most small-signal transistors are rated 25V–40V minimum · IC_max ≥ Iout with safety margin (e.g. BC547 handles 100mA, easily handles 1mA) High hFE (current gain) — reduces base current error (see limitations section)
Accounting for Base Current Error
Given that Vbe and beta for both transistors is the same, the base current for each transistor must also be the same. Since the transistors are operated in their linear regions, the current through Rp is split between the collector and the branch feeding the two bases. This base current error represents one of the primary limitations of the basic two-transistor current mirror.
The output current relationship accounting for finite beta (β) can be expressed as:
IOUT = IREF × β²/(β² + 2β)
Note that this equation predicts that IO < IREF unless β →∞. For typical transistors with β = 100, this results in approximately 2% error in the mirrored current.
Performance Characteristics and Limitations
Output Impedance
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. The second is its AC output resistance, which determines how much the output current varies with the voltage applied to the mirror.
A current mirror has high output impedance because its output node is configured so that changes in output voltage produce only small changes in output current. High output impedance arises from the device physics and the circuit topology that decouples current from voltage at the mirror output.
Early Effect and Output Resistance
The VCB of Q1 in the mirror is zero. If VCB is greater than zero in the output transistor Q2, the collector current in Q2 will be somewhat larger than Q1 due to the Early effect. One of the flaws in the ointment is the Early effect of collector voltage on collector current. It can sometimes be estimated from datasheet parameters if output admittance (hoe) is specified (Ee ~ hoe / test current). A representative value is 1% per volt.
Because the Early effect has been neglected in solving for IO, the output resistance is infinite. If we include the Early effect and assume that it has negligible effect in the solution for IO, the output resistance is given by the Early voltage divided by the output current. This finite output resistance causes the mirrored current to vary slightly with changes in output voltage.
Compliance Voltage
The minimum voltage drop across the output part of the mirror necessary to make it work properly. This minimum voltage is dictated by the need to keep the output transistor of the mirror in active mode. The range of voltages where the mirror works is called the compliance range and the voltage marking the boundary between good and bad behavior is called the compliance voltage.
It is necessary to keep the output (BJT) transistor out of saturation, VCB = 0 V. Or from another perspective, not allow the collector base junction to forward bias. That means the lowest output voltage that results in the correct output current, the compliance voltage, is VOUT = VCV = VBE under bias conditions with the output transistor at the output current level IC and with VCB = 0 V
Temperature Sensitivity
the current mirror is often used in bipolar circuits such as low voltage bipolar amplifier circuits. a problem in low voltage applications stems from variations in base-emitter voltage, V be , with temperature, which can adversely affect a reference current and a mirrored current. the current through transistor Q rf increases as V be is reduced at about −2 mV/° C. for a silicon bipolar transistor or −1 mV/° C. for a GaAs heterojunction bipolar transistor.
In this paper, an accurate current reference using temperature and process compensation current mirror (TPC-CM) is proposed. The temperature independent reference current is generated by summing a proportional to absolute temperature (PTAT) current and a complementary to absolute temperature (CTAT) current. This compensation technique can significantly improve temperature stability in precision applications.
Improved Current Mirror Topologies
Emitter Degeneration
of obtaining a better match between the input and output currents is to use series emitter resistors on the transistors. If the current in one transistor increases, it causes the voltage across its emitter resistor to increase, which causes a decrease in its base-emitter voltage. This causes the current to decrease, thus causing the two transistors to have more equal currents. A typical value for the emitter resistors might be 100 Ω.
A first step is to connect resistors to the emitters (or the sources, in the case of MOS transistors), as illustrated in Figure 4-7. With the 6 kΩ resistances we’re using in this example, we drop 300 mV across the resistors. If the current in Q2 wants to be higher than I1, it would also cause a higher voltage drop across R2. This increased voltage drop across R2 decreased the base-emitter voltage (VBE) of Q2. This negative feedback effect forces I2 back to where it’s more or less equal to I1.
When unmatched (typically discrete) transistors are used for a mirror, it has long been known that resistive emitter degeneration yields a much more predictable result and a higher effective output impedance, combating the Early effect. However, this improvement comes at the cost of reduced voltage headroom and increased minimum compliance voltage.
Base Current Compensation
Figure 3 shows the basic current mirror with a third transistor added. Figure 3: Mirror with base current compensation. This three-transistor configuration significantly reduces the base current error that plagues the basic two-transistor design.
Figure 11.8 shows a mirror where the simple wire connecting the collector of Q1 to its base is replaced by an emitter follower buffer. This improvement to the simple current mirror is referred to as an emitter follower augmented mirror. The current gain (ßQ3) of the emitter follower buffer stage (Q3) greatly reduces the gain error caused by the finite base currents of Q1 and Q2.
Wilson Current Mirror
The circuit is named after George R. Wilson, an integrated circuit design engineer who worked for Tektronix. Wilson devised this configuration in 1967 when he and Barrie Gilbert challenged each other to find an improved current mirror overnight that would use only three transistors. Wilson won the challenge.
The Wilson current mirror has the particular advantages over alternatives that: The static error, the input-output current difference, is reduced to very small levels attributable almost entirely to random device mismatches while the output impedance is raised by a factor of … The circuit uses minimum resources.
Removes base current mismatch: Unlike simple current mirror designs, the Wilson configuration gets close to eliminating base current balance errors. This results in an output current accuracy close to the input current reference. High Output Impedance: The circuit employs very high output impedance because of the negative feedback from T3 base to T1, far superior to the simple two-transistor current mirrors.
An even greater improvement can be made with the addition of a transistor. This circuit, invented by George Wilson, is naturally called the Wilson Current Mirror (analog designers don’t get Nobel prizes, they get a circuit named after them).
Improved Wilson Mirror
Adding a fourth transistor to the simple Wilson current mirror in figure 11.10, we have the modified or improved Wilson mirror. The improved input to output current accuracy is accomplished by equalizing the collector voltages of Q1 and Q2 at 1 VBE. This leaves the finite ß and voltage differences of each of Q1 and Q2 as the remaining unbalancing influences in the mirror.
There’s still a systematic error in the basic Wilson current mirror: the two transistors intended to match don’t have the same collector voltages. One transistor is at VBE; the other is at 2VBE. Enter a fourth transistor (Figure 4-12). The only purpose of Q4 is to lower the collector voltage of Q1 to the same level as that of Q2. With this, we see in Figure 4-13 that I2 is now within 0.6% of I1 and changes by less than 0.08% over the output voltage range.
Widlar Current Source
A Widlar current source is a modification of the basic two-transistor current mirror that incorporates an emitter degeneration resistor for only the output transistor, enabling the current source to generate low currents using only moderate resistor values. This circuit is named for its inventor, Robert Widlar, and was patented in 1967. The Widlar circuit may be used with bipolar transistors or MOS transistors. An example application is in the now famous uA741 operational amplifier, and Widlar used the circuit in many of his designs.
Figure 11.11 is an example Widlar current source using bipolar transistors, where the emitter resistor R2 is connected in series with the emitter of output transistor Q2, and has the effect of reducing the current in Q2 relative to Q1. This topology is particularly useful when very low output currents are required without using impractically large resistor values.
Cascode Current Mirror
The cascode current mirror configuration stacks additional transistors to dramatically increase output impedance. Cascoding further multiplies output resistance when extremely high Rout is required. Cascode mirror: Rout increases roughly by the cascode’s intrinsic gain factor, producing Rout >> ro of a single device.
The cascode raises the output impedance by about two orders of magnitude, greatly improving performance. It also enables Q1 and Q2 to have very similar operating conditions, which also improves performance. This makes cascode mirrors ideal for applications requiring very stable current sources with minimal sensitivity to voltage variations.
The main limitation of BJT cascode mirror is that the systematic gain error stemming from finite beta was large. To overcome this limitation, the wilson mirror is used. The choice between cascode and Wilson configurations depends on the specific application requirements and performance priorities.
Applications of BJT Current Mirrors
Biasing Networks
The current mirror is used to provide bias currents and active loads to circuits. Current mirrors are extensively used to establish stable operating points for transistors in amplifier stages. Unlike resistive biasing, current mirror biasing provides superior power supply rejection and temperature stability.
While resistors can be manufactured in ICs, it is easier to fabricate transistors. IC designers avoid some resistors by replacing load resistors with current sources. A circuit like an operational amplifier built from discrete components will have a few transistors and many resistors. An integrated circuit version will have many transistors and a few resistors. This fundamental difference drives the widespread use of current mirrors in integrated circuit design.
Active Loads in Differential Amplifiers
Many IC amplifiers use BJT loads in place of the load resistance, RC. BJT load resistor is usually connected as a constant-current source with a very high resistance load (output resistance of the current source) • Higher load resistance, higher output gain. Left figure shows an AMP with active load (consisting of Q3 and Q4).
A differential amplifier features two BJT transistors Q1 and Q2 whose emitter terminals are connected together and to a current source. When closely matched BJTs are used, common-mode amplification is extremely small and if these devices are thermally closely coupled, temperature changes only have the same effect as applying a slow-changing common-mode input voltage. The differential amplifier circuit shown in Figure 3 also uses two current mirrors – one for biasing and the other acting as the gain component for a single-ended output.
The current mirror active load produces a very high internal impedance, thus contributing to a very high differential gain. This configuration is fundamental to operational amplifier input stages and other high-gain analog circuits.
Operational Amplifier Design
Most modern operational amplifiers utilize a differential amplifier front end. In other words, the first stage of the operational amplifier is a differential amplifier. Current mirrors play multiple critical roles in op-amp design, including tail current sources for differential pairs, active loads for voltage gain stages, and output stage biasing.
Often, the collector load of a transistor is not a resistor but a current mirror. For example the collector load of Q4 collector, Ch 8 is a current mirror (Q2). For an example of a current mirror with multiple collector, outputs see Q13 in the model 741 op-amp, Ch 8. The Q13 current mirror outputs substitute for resistors as collector loads for Q15 and Q17.
Current Steering and Signal Processing
Current mirrors enable sophisticated current steering techniques in analog multipliers, digital-to-analog converters, and other precision analog circuits. Digital-to-analog converters: Current mirrors can be used in digital-to-analog converter circuits to provide a precise current source that is proportional to the digital input code.
In analog multipliers and variable gain amplifiers, current mirrors allow precise control of signal currents while maintaining high linearity and low distortion. The ability to scale currents by transistor area ratios makes current mirrors ideal for implementing weighted current sources in DAC ladder networks.
Voltage Regulators and References
Voltage regulators: Current mirrors can be used in voltage regulator circuits to provide a constant current to a load, regardless of changes in the input voltage or load resistance. Bandgap voltage references, which are fundamental to precision analog systems, rely heavily on current mirror circuits to generate temperature-compensated reference voltages.
Current mirrors also serve as essential building blocks in low-dropout (LDO) regulators, providing stable bias currents for error amplifiers and pass transistors while maintaining high power supply rejection ratios.
Current Sensing Applications
Many applications like electric (EV) or mild-hybrid vehicles (HEV) for example, require the load current being drawn from a battery to be sensed close to the battery itself. The current must be converted to a voltage that is within the input range of an analog-to-digital converter (ADC) or a microcontroller and therefore it must have a small magnitude. This can be done using the current sensing circuit shown in Figure 5 where V1 represents the 48 V battery voltage and I1 is the load current drawn from it. Clearly, this circuit is based on two current mirrors – one pair of NPN BJTs and another pair of PNPs. A load is connected to the battery via a 50 mΩ current sensing resistor which means that for a maximum load current of 10 A, the input voltage to the sensing circuit will be 0.5 V.
LED Drivers and Display Applications
Set a precise current through an LED using a current mirror. Unlike a simple resistor (whose current changes with supply voltage and LED VF variation), a current mirror maintains exactly the set current regardless of supply fluctuations — making LED brightness consistent. This application is particularly important in display backlighting, indicator lights, and automotive lighting systems where consistent brightness is critical.
Design Considerations and Best Practices
Layout Techniques for Matching
Careful layout and transistor design must be used to minimize this source of error. For example, Q1 and Q2 may each be implemented as a pair of paralleled transistors arranged as a cross-coupled quad in a common-centric layout to reduce effects of local gradients in current gain. If the mirror is to be used at a fixed bias level, matching resistors in the emitters of this pair can transfer some of the matching problem from the transistors to those resistors.
The die pairs in each package are specifically harvested from the same wafer area to minimize the possibility of deviations in the manufacturing process. In integrated circuit design, common-centroid layout techniques and interdigitated transistor structures help minimize the effects of process gradients and thermal gradients across the die.
Thermal Management
Further, Q2 may get substantially hotter than Q1 due to the associated higher power dissipation. To maintain matching, the temperature of the transistors must be nearly the same. In integrated circuits and transistor arrays where both transistors are on the same die, this is easy to achieve. But if the two transistors are widely separated, the precision of the current mirror is compromised.
For discrete implementations, physical proximity and thermal coupling are essential. Mounting matched transistors on the same heat sink or using dual transistor packages ensures thermal tracking. In high-power applications, careful thermal design prevents temperature differentials that would degrade matching accuracy.
Power Supply Considerations
The minimum supply voltage for a current mirror must accommodate the compliance voltage plus any voltage drops across current-setting resistors. For basic mirrors, this typically requires at least VBE + VCE,sat, approximately 1V for silicon BJTs. More complex topologies like Wilson or cascode mirrors require additional headroom.
Power supply noise can couple into the reference current, degrading mirror performance. Proper decoupling capacitors and careful power distribution network design minimize these effects. In precision applications, using a separate regulated supply for the reference current can significantly improve performance.
Frequency Response and Stability
Frequency Response Problems: High-frequency operation creates instability in the negative feedback loop. The parasitic capacitances of the transistors, particularly base-collector capacitance, can create poles in the transfer function that limit bandwidth or cause instability in feedback configurations.
Another consequence of adding the emitter follower buffer is, in general, a loss in the frequency response of the mirror. Transistor Q3 is potentially operating at a very small current of 2IB. If there were to be a significant capacitance to ground at the base connection common to Q1 and Q2 the current available to discharge this current will also be small equal to 2IB. Careful attention to parasitic capacitances and operating currents is essential for high-frequency applications.
Advanced Topics and Modern Developments
Low-Voltage Operation
This difference is increased when the transistors share a common body terminal and the body effect in M4 raises its threshold voltage. On the output side of the mirror, the minimum voltage to ground is … This voltage is likely to be significantly greater than 1.0 volts. Both potential differences leave insufficient headroom for the circuitry that provides the input current and uses the output current unless the power supply voltage is higher than 3 volts. Many contemporary integrated circuits are designed to use low voltage power supplies to accommodate the limitations of short-channel transistors, to meet the need for battery operated devices and to have high power efficiency in general. The result is that new designs tend to use some variant of a wide swing cascode current mirror configuration.
Modern low-voltage designs employ specialized topologies that minimize voltage headroom requirements while maintaining adequate performance. These include gain-boosted mirrors, regulated cascode configurations, and adaptive biasing schemes that optimize performance across varying supply voltages.
Process Compensation Techniques
The temperature coefficient and magnitude of the reference current are influenced by the process variation. To calibrate the process variation, the proposed TPC-CM uses two binary weighted current mirrors which control the temperature coefficient and magnitude of the reference current. After the PTAT and CTAT currents are measured, the switch codes of the TPC-CM are fixed in order that the magnitude of reference current is independent to temperature. And, the codes are stored in the non-volatile memory. In the simulation, the effect of the process variation is reduced to 0.52% from 19.7% after the calibration using a TPC-CM in chip-by-chip.
Digital trimming and calibration techniques allow modern current mirrors to achieve precision levels previously unattainable. By measuring and compensating for process variations during production testing, manufacturers can guarantee tight specifications across production lots and operating conditions.
High Output Impedance Designs
The current mirror is one of the key elements in analog circuit design. For high performance analog circuit applications, the accuracy and output impedance are the most important parameters to determine the performance of the current mirror. In this paper, a new current mirror is proposed to provide high accuracy and very high output impedance. A novel feedback gain stage is used to increase the output impedance and matching accuracy significantly. Moreover, the proposed new current mirror also has an output swing similar to the traditional two-stage cascode current mirror.
Advanced topologies employ multiple feedback loops and gain-boosting techniques to achieve output impedances in the gigaohm range. These ultra-high impedance mirrors are essential for precision instrumentation, high-resolution data converters, and other applications where current source quality directly impacts system performance.
Troubleshooting and Common Pitfalls
Mismatch Issues
k1 is called the current factor and ideally, it should have a value of 1 or another value determined by the ratio between the selected values for R1 and R2. IOUT should track IIN across the range of input current values required by the design, however, even small differences in the physical characteristics of the BJTs, like for example, if they have different values of VBE and/or hfe then k1 will deviate from the desired value. This makes it more difficult to precisely control IOUT and therefore to define the behavior of the circuit it is biasing.
When troubleshooting current mirror circuits, verify that transistors are properly matched and operating in their active regions. Measure VBE voltages to confirm matching, and check collector voltages to ensure neither transistor has entered saturation. Temperature differences between transistors often manifest as systematic current errors that vary with power dissipation.
Saturation and Compliance
One of the most common failures in current mirror circuits occurs when the output transistor enters saturation due to insufficient collector-emitter voltage. This typically happens when the load resistance is too large or the supply voltage too low. Always verify that the output voltage remains above the compliance voltage under all operating conditions.
In circuits with varying loads, dynamic compliance violations can occur during transients. Adding bypass capacitors and ensuring adequate voltage margins prevents these issues. For critical applications, monitoring circuits can detect compliance violations and trigger protective actions.
Oscillation and Instability
Current mirrors with feedback, particularly Wilson configurations, can oscillate if parasitic capacitances create excessive phase shift. Small compensation capacitors across critical nodes can stabilize the circuit. However, excessive compensation degrades frequency response, requiring careful optimization.
Ground loops and poor power supply decoupling can inject noise into the reference current, causing output current variations. Star grounding techniques and local decoupling capacitors minimize these effects. In mixed-signal systems, separating analog and digital grounds prevents digital switching noise from corrupting analog currents.
Measurement and Characterization
DC Characterization
To fully characterize a current mirror, measure the output current versus output voltage across the full compliance range. This I-V curve reveals the compliance voltage, output impedance, and any non-ideal behavior. Sweep the reference current to verify linearity and current gain accuracy across the operating range.
Temperature characterization requires measurements across the specified temperature range, typically -40°C to +125°C for commercial applications. Plot output current versus temperature at fixed reference current and output voltage to quantify temperature coefficient. Well-designed mirrors should exhibit temperature coefficients below 100 ppm/°C.
AC Performance
AC characterization involves measuring output impedance versus frequency and determining the bandwidth of the current mirror. Small-signal AC analysis reveals poles and zeros in the transfer function. For mirrors used in dynamic applications, transient response measurements show settling time and overshoot characteristics.
Noise measurements are critical for precision applications. Measure output current noise spectral density across the frequency range of interest. Flicker noise dominates at low frequencies, while thermal noise sets the noise floor at higher frequencies. Proper biasing and device sizing minimize noise contributions.
Practical Design Resources
For engineers designing BJT current mirrors, several excellent resources provide additional depth and practical guidance. The Analog Devices website offers extensive application notes and design tools for current mirror circuits. Texas Instruments provides comprehensive analog design guides covering current sources and biasing techniques.
For hands-on learning, breadboarding simple current mirror circuits with discrete components provides invaluable intuition. Start with a basic two-transistor mirror using matched small-signal transistors like the BC547 or 2N3904. Measure performance, then progressively implement improved topologies to observe the benefits firsthand.
SPICE simulation tools enable detailed analysis before committing to hardware. Modern simulators include Monte Carlo analysis for evaluating the effects of component tolerances, temperature sweeps for thermal characterization, and AC analysis for frequency response. These tools help optimize designs and identify potential issues early in the development process.
Conclusion
BJT current mirrors represent fundamental building blocks in analog circuit design, offering elegant solutions for current replication, biasing, and active loading. While the basic two-transistor configuration provides a simple starting point, understanding the limitations and available improvements enables designers to select appropriate topologies for specific applications.
From simple biasing networks to sophisticated operational amplifiers, current mirrors enable functionality that would be impractical or impossible with passive components alone. The ability to generate precise, stable currents with minimal silicon area makes current mirrors indispensable in modern integrated circuit design.
Success with current mirror design requires attention to transistor matching, thermal management, layout techniques, and operating conditions. By applying the principles and calculations outlined in this guide, engineers can design robust current mirrors that meet demanding performance specifications across temperature, process variations, and operating conditions.
As semiconductor technology continues to advance toward lower voltages and smaller geometries, current mirror design evolves to address new challenges. Low-voltage topologies, digital calibration techniques, and advanced compensation methods ensure that current mirrors remain relevant and effective in next-generation analog and mixed-signal systems.